Publications
 Books Brownian Motion and its Applications to Mathematical Analysis. École d'Été de Probabilités de Saint-Flour XLIII - 2013, Springer, New York, 2014. The Search for Certainty. On the Clash of Science and Philosophy of Probability. World Scientific, Hackensack, NJ, 2009. Cutting Brownian paths Memoir AMS, 95pp., Number 657, Volume 137, American Mathematical Society, Providence, RI, January 1999 (with R. Bass) Math review 99g:60146 Seminar on Stochastic Processes 1992, 276pp., Birkhäuser, Boston 1993 (managing editor, with R. Bass) Math review 94m:60003 Multidimensional Brownian Excursions and Potential Theory, 172pp. Longman, London 1987 Math review 89d:60146 Research articles The distribution of the spine of a Fleming-Viot type process (preprint, with M. Bieniek) (Math ArXiv version) Can one make a laser out of cardboard? (preprint, with T. Tadic) (Math ArXiv version) Stirring two grains of sand Electr. J. Probab. 20 (2015) 1-29, article 13. A Lorentz model with variable density in a gravitational field: limit theorems and recurrence (preprint, with D. Rizzolo) (Math ArXiv version) Meteor process on ${\mathbb Z}^d$ Probab. Theory Rel. Fields (to appear) (Math ArXiv version) Comparison of quenched and annealed invariance principles for random conductance model: Part II. A Festschrift in Honor of Masatoshi Fukushima. World Scientific, 2014. (to appear, with M. Barlow and A. Timar) (Math ArXiv version) On meteors, earthworms and WIMPs Ann. Appl. Probab. 25 (2015) 1729-1779 (with S. Billey, S. Pal and B. Sagan) Fractal trace of earthworms Phys. Rev. E 87 no. 5, May 2013 (with R. Holyst and L. Pruski) Comparison of quenched and annealed invariance principles for random conductance model Probab. Theory Rel. Fields (to appear, with M. Barlow and A. Timar) (Math ArXiv version) Forward Brownian motion Probab. Theory Rel. Fields 160 (2014) 95-126 (with M. Scheutzow) Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion Probab. Theory Rel. Fields 159 (2014) 237-272 (with D. Nualart and J. Swanson) Permutations with given peak set Journal of Integer Sequences 16 (2013) Article 13.6.1 (with S. Billey and B. Sagan) Rubber bands, pursuit games and shy couplings Proc. London Math. Soc. 109 (2014) 121-160 (with M. Bramson and W. Kendall) Invisibility via reflecting coating J. London Math. Soc. 88 (2013) 359-374 (with T. Kulczycki) Deterministic approximations of random reflectors Trans. Amer. Math. Soc. 365 (2013) 6367-6383 (with O. Angel and S. Sheffield) Extinction of Fleming-Viot-type particle systems with strong drift Electron. J. Probab. 17 (2012), paper 11, 1-15 (with M. Bieniek and S. Pal) Reflecting random walk in fractal domains Ann. Probab. 41 (2013) 2791-2819 (with Z. Chen) Brownian earthworm Ann. Probab. 41 (2013) 4002-4049 (with Z. Chen and S. Pal) Isolated zeros for Brownian motion with variable drift Electron. J. Probab. 16 (2011), paper 65, 1793-1815 (with T. Antunovic, Y. Peres and J. Ruscher) Stationary distributions for jump processes with memory Ann. I. H. Poincaré 48 (2012) 609-630 (with T. Kulczycki and R. Schilling) Stationary distributions for jump processes with inert drift, Malliavin Calculus and Stochastic Analysis: A Festschrift in Honor of David Nualart, Springer Proceedings in Mathematics & Statistics 34, Springer, New York, 2013, 139-172 (with T. Kulczycki and R. Schilling) Non-uniqueness for non-negative solutions of parabolic stochastic partial differential equations Illinois J. Math., Burkholder Volume 54 (2010) 1481-1507 (with C. Mueller and E. Perkins) Shy Couplings, CAT(0) Spaces, and the Lion and Man Ann. Probab. 41 (2013) 744-784 (with M. Bramson and W. Kendall) Comment on article by Robert Bayesian Analysis 5 (2010) 233-236. Crowding of Brownian spheres ALEA Lat. Am. J. Probab. Math. Stat. 7 (2010) 193-205 (with S. Pal and J. Swanson) Archimedes' principle for Brownian liquid Ann. Appl. Probab. 21 (2011) 2053-2074 (with Z. Chen and S. Pal) Markov processes on time-like graphs Ann. Probab. 39 (2011) 1332-1364 (with S. Pal) Non-extinction of a Fleming-Viot particle model Probab. Theory Rel. Fields 153 (2012) 293-332 (with M. Bieniek and S. Finch) Differentiability of stochastic flow of reflected Brownian motions Electron. J. Probab. 14 (2009) 2182-2240. Multiplicative functional for reflected Brownian motion via deterministic ODE Illinois J. Math., Burkholder Volume, 54 (2010) 895-925 (with J. Lee) Stationary distributions for diffusions with inert drift Probab. Theory Rel. Fields 146 (2010) 1-47 (with R. Bass, Z. Chen and M. Hairer) A change of variable formula with Ito correction term Ann. Probab. 38 (2010) 1817-1869 (with J. Swanson) The Skorokhod problem in a time-dependent interval Stoch. Process. Appl. 119 (2009) 428-452 (with W. Kang and K. Ramanan) Markov processes with product-form stationary distribution Electron. Comm. Probab. 13 (2008) 614-627 (with D. White) On pathwise uniqueness for reflecting Brownian motion in $C^{1+\gamma}$ domains Ann. Probab. 36 (2008) 2311-2331 (with R. Bass) Brownian motion with inert drift, but without flux: a model Physica A 384 (2007) 278-284 (with R. Holyst and L. Pruski) Discrete approximations to reflected Brownian motion Ann. Probab. 36, (2008) 698-727 (with Z. Chen) Mirror couplings and Neumann eigenfunctions Indiana U. Math. J. 57 (2008) 1317-1353. (with R. Atar) Pathwise uniqueness for a degenerate stochastic differential equation Ann. Probab. 35, (2007) 2385-2418 (with R. Bass and Z. Chen) Pathwise uniqueness for two dimensional reflecting Brownian motion in certain planar Lipschitz domains Electr. Comm. Probab. 11 (2006) paper 18, pages 178-181. (with R. Bass) Shy couplings Probab. Theory Rel. Fields 137 (2007) 345-377. (with I. Benjamini and Z. Chen) Comparison of potential theoretic properties of rough domains Proc. AMS 134 (2006), 3247-3253. On the Robin problem in fractal domains Proc. London Math. Soc. 96 (2008), 273-311 (with R. Bass and Z. Chen) An annihilating-branching particle model for the heat equation with average temperature zero Ann. Probab. 34, (2006) 2382-2405 (with J. Quastel) Synchronous couplings of reflected Brownian motions in smooth domains Illinois J. Math., Doob Volume 50 (2006) 189-268 (with Z. Chen and P. Jones) Neumann eigenfunctions and Brownian couplings Potential theory in Matsue. Proceedings of the International Workshop on Potential Theory, Matsue 2004. Advanced Studies in Pure Mathematics 44. Mathematical Society of Japan, 2006, pp. 11-23 (review paper) A Gaussian oscillator Electron. Comm. Probab. 9 (2004), paper 10, pp. 92-95 (with D. White) The "hot spots" problem in planar domains with one hole. Duke Math. J. 129 (2005) 481-502 The heat equation in time dependent domains with insulated boundaries J. Math. Anal. Appl. 294 (2004) 581-595 (with Z. Chen and J. Sylvester) Coalescence on the high-dimensional sphere: a caricature for perfect simulation. Symposium in Honour of Ole E. Barndorff-Nielsen (Aarhus, 2000), 50-52, Memoirs, 16, Univ. Aarhus, Aarhus, 2000 (with W. Kendall) Traps for reflected Brownian motion Math. Z. 252 (2006) 103-132 (with Z. Chen and D. Marshall) The heat equation and reflected Brownian motion in time dependent domains. II. Singularities of solutions J. Func. Anal. 204 (2003) 1-34 (with Z. Chen and J. Sylvester) Lenses in skew Brownian flow Ann. Probab. 32 (2004) 3085-3115 (with H. Kaspi) Stochastic differential equations driven by stable processes for which pathwise uniqueness fails Stoch. Proc. and their Appl. 111 (2004) 1-15 (with R. Bass and Z. Chen) Erratum to "The supremum of Brownian local times on Hölder curves" Ann. I. H. Poincaré 38 (2002) 799-800 (with R. Bass) Super-Brownian motion with reflecting historical paths. II. Convergence of approximations Probab. Theory Rel. Fields 133 (2005) 145-174 (with L. Mytnik) Uniqueness for reflecting Brownian motion in lip domains Ann. I. H. Poincaré 41 (2005) 197-235 (with R. Bass and Z. Chen) On nodal lines of Neumann eigenfunctions Electron. Comm. Probab. 7, (2002) paper 14, p. 129-139 (with R. Atar) On Neumann eigenfunctions in lip domains Journal AMS 17 (2004) 243-265 (with R. Atar) Shocks and business cycles Advances in Theoretical Economics 5 (2005) 1-86, no. 1, article 2 (with D. Frankel) Censored stable processes Probab. Theory Rel. Fields 127 (2003) 89-152 (with K. Bogdan and Z. Chen) Mechanisms for facilitated target location and the optimal number of molecules in the diffusion search process Phys. Rev. E 64 (2001) article no. 011914 (with R. Holyst) Coalescence of synchronous couplings Probab. Theory Rel. Fields 123 (2002) 553-578 (with Z. Chen) Stable processes have thorns Ann. Probab. 31 (2003) 170-194 (with T. Kulczycki) Brownian motion reflected on Brownian motion Probab. Theory Rel. Fields 122 (2002) 471-493 (with D. Nualart) The heat equation and reflected Brownian motion in time dependent domains Ann. Probab.32 (2004) 775-804 (with Z. Chen and J. Sylvester) Super-Brownian motion with reflecting historical paths Probab. Theory Rel. Fields 121 (2001) 447-491 (with J.-F. Le Gall) The supremum of Brownian local times on Hölder curves Ann. Inst. Henri Poincaré 37 (2001) 627-642 (with R. Bass) Reduction of dimensionality in a diffusion search process and kinetics of gene expression Physica A, 277 (2000) 71-82) (with R. Holyst, M. Blazejczyk, G. Goralski and L. Bocquet) Coalescence of skew Brownian motions Seminaire de Probabilites XXXV, LNM 1755 (2001) 202-205 (with M. Barlow, H. Kaspi and A. Mandelbaum) A Fleming-Viot particle representation of Dirichlet Laplacian Comm. Math. Phys. 214 (2000) 679-703 (with R. Holyst and P. March) Diffusion on curved periodic surfaces Phys. Rev. E 60 (1999) 302-307 (with R. Holyst, D. Plewczynski and A. Aksimentiev) Fiber Brownian motion and the `hot spots' problem Duke Math. J. 105 (2000) 25-58 (with R. Bass) Math review 2001g:60190 Local time flow related to skew Brownian motion Ann. Probab. 29 (2001) 1693-1715 (with Z.-Q. Chen) Variably skewed Brownian motion Electr. Comm. Probab. 5, (2000) paper 6, p. 57-66. (with M. Barlow, H. Kaspi and A. Mandelbaum) Math review 2001j:60146 Weak convergence of reflecting Brownian motions Electr. Comm. Probab. 3, (1998) paper 4, p. 29-33 (with Z.-Q. Chen) Math review 99d:60091 Efficient Markovian couplings: examples and counterexamples Ann. Appl. Probab. 10 (2000) 362-409. (with W. Kendall) A counterexample to the "hot spots" conjecture Ann. Math. 149 (1999) 309-317 (with W. Werner) Math review 2000b:35044 Stochastic bifurcation models Ann. Probab. 27 (1999) 50-108 (with R. Bass) Math review 2000b:60201 On minimal parabolic functions and time-homogeneous parabolic $h$-transforms Trans. Amer. Math. Soc. 351 (1999) 3499-3531 (with T. Salisbury) Math review 99m:60113 Positivity of Brownian transition densities Electr. Comm. Probab. 2 (1997) paper 4, p. 41-53 (with M. Barlow and R. Bass) Math review 99e:60166 On the time and direction of stochastic bifurcation. In Asymptotic Methods in Probability and Statistics. A Volume in Honour of Miklos Csorgo. B. Szyszkowicz, ed., pp. 483-500. Elsevier, Amsterdam, 1998. (with D. Frankel and A. Pauzner) Math review 99k:60148 Brownian motion in a Brownian crack Ann. Appl. Probab. 8 (1998) 708-748 (with D. Khoshnevisan) Math review 99g:60147 On the "hot spots" conjecture of J. Rauch J. Func. Anal. 164 (1999) 1-33 (with R. Bañuelos) Math review 2000m:35085 Fast equilibrium selection by rational players living in a changing world Econometrica 69 (2001) 163-190 (with D. Frankel and A. Pauzner) Sets avoided by Brownian motion Ann. Probab. 26 (1998) 429-464 (with O. Adelman and R. Pemantle) Math review 99i:60152 Configurational transition in a Fleming-Viot-type model and probabilistic interpretation of Laplacian eigenfunctions J. Phys. A 29, 1996, 2633-2642. (with R. Holyst, D. Ingerman and P. March) Eigenvalue expansions for Brownian motion with an application to occupation times, Electronic Journal of Probability 1, 1996, Paper 3, 1-19. (with R. Bass) Math review 97c:60201 A critical case for Brownian slow points Probab. Th. Rel. Fields 105, 1996, 85-108. (with R. Bass) Math review 97m:60054 The level sets of iterated Brownian motion Seminaire de Probabilites XXIX, J. Azéma, M. Emery, P.A. Meyer, M. Yor, eds., 1995, 231-236. (with D. Khoshnevisan) Math review 98k:60138 No triple point of planar Brownian motion is accessible Ann. Probab. 24, 1996, 125-147 (with W. Werner) Math review 97j:60147 Ito formula for an asymptotically 4-stable process Ann. Appl. Probab. 6, 1996, 200-217 (with A. Madrecki) Math review 99a:60042 Sur quelques filtrations et transformations browniennes Seminaire de Probabilites XXIX, J. Azéma, M. Emery, P.A. Meyer, M. Yor, eds., 1995, 56-69. (with S. Attal, M. Émery and Y. Hu) Math review 98j:60111 Iterated law of iterated logarithm Ann. Probab. 23, 1995, 1627--1643 (with J. San Martin) Math review 97d:60075 Labyrinth dimension of Brownian trace (invited paper) Probability and Mathematical Statistics. Volume Dedicated to the Memory of Jerzy Neyman. 15, 1995, 165-193. Math review 97j:60146 Conditioned Brownian motion in planar domains Probab. Th. Rel. Fields 101, 1995, 479-493 (with R. Bass) Math review 96b:60199 2-D Brownian motion in a system of reflecting barriers: effective diffusivity by a sampling method J. Phys. A: Math. General 27, 1994, 631-644. (with R. Holyst and D. Ingerman) An asymptotically 4-stable process J. Fourier Anal. Appl. Special Issue. Proceedings of the Conference in Honor of J.-P. Kahane, 1995, 97-117. (with A. Madrecki) Math review 96j:60072 A Skorohod-type lemma and a decomposition of reflected Brownian motion Ann. Probab. 23, 1995, 586-604 (with E. Toby) Math review 96i:60045 Excursion laws and exceptional points on Brownian paths. Seminaire de Probabilites XXVII, J. Azéma, P.A. Meyer, M. Yor, eds., Springer, Berlin, 1993, 177-181. Math review 95m:60118 Variation of iterated Brownian motion. Measure-Valued Processes, Stochastic Partial Differential Equations and Interacting Systems, D.A. Dawson, ed., CRM Proceedings and Lecture Notes 5, 1994, 35-53. Math review 95h:60123 On domain monotonicity of the Neumann heat kernel. J. Func. Anal. 116, 1993, 215-224 (with R. Bass) Math review 94k:60120 Some path properties of iterated Brownian motion. Seminar on Stochastic Processes 1992 K.L. Chung, E. Cinlar and M.J. Sharpe, eds., Birkhäauser, Boston, 1993, 67-87. Math review 95c:60075 Intersection local time for points of infinite multiplicity. Ann. Probab. 22, 1994, 566-625 (with R. Bass and D. Khoshnevisan) Math review 95j:60118 A three-dimensional Brownian path reflected on a Brownian path is a free Brownian path. Letters Math. Phys. 27, 1993, 239-241 Math review 94c:60132 2-D Brownian motion in a system of traps: Application of conformal transformations. J. Phys. A: Math. General 25, 1992, 2463-2471 (with R. Holyst and T. Salisbury) The boundary Harnack principle for non-divergence form elliptic operators. J. London Math. Soc. 50, 1994, 157-169 (with R. Bass) Math review 95f:35058 Non-polar points for reflected Brownian motion. Ann. Inst. Henri Poincaré 29, 1993, 199-228 (with D. Marshall) Math review 94g:60152 The Martin boundary in non-Lipschitz domains. Trans. Amer. Math. Soc. 337, 1993, 361-378 (with R. Bass) Math review 93g:31019 Hölder domains and the boundary Harnack principle. Duke Math. J. 64, 1991, 195-200 (with R. Bañuelos and R. Bass) Math review 92g:35077 Hitting a boundary point with reflected Brownian motion. Seminaire de Probabilites XXVI, J. Azéma, P.A. Meyer, M. Yor, eds., 1992, 81-94. (with D. Marshall) Math review 94g:60151 Lifetimes of conditioned diffusions. Probab. Th. Rel. Fields 91, 1992, 405-443. (with R. Bass) Math review 93e:60155 A boundary Harnack principle in twisted Hölder domains. Ann. Math. 134, 1991, 253-276 (with R. Bass) Math review 92m:31006 Rigorous exponent inequalities for random walks. J. Phys. A: Math. Gen. 23, 1990, L23-L28 (with G. Lawler) Math review 91a:60271 A probabilistic proof of the boundary Harnack principle. Seminar on Stochastic Processes 1989 K.L. Chung, E. Cinlar and R. Getoor, eds., Birkhäuser, Boston, 1990, 1-16 (with R. Bass) Math review 92c:60106 A representation of local time for Lipschitz surfaces. Probab. Th. Rel. Fields 84, 1990, 521-547 (with R. Bañuelos and R. Bass) Math review 91f:60139 On non-increase of Brownian motion. Ann. Probab. 18, 1990, 978-980. Math review 91e:60234 Non-intersection exponents for Brownian paths. Part II. Estimates and applications to a random fractal. Ann. Probab. 18, 1990, 981-1009. (with G. Lawler) Math review 91g:60097 Non-intersection exponents for Brownian paths. Part I. Existence and an invariance principle. Probab. Th. Rel. Fields 84, 1990, 393-410 (with G. Lawler) Math review 91g:60096 On the critical exponent for random walk intersections. J. Stat. Phys. 56, 1989, 1-12 (with G. Lawler and T. Polaski) Math review 91h:60073 Brownian crossings between spheres, J. Math. Anal. Appl. 148, 1990, 101-120 (with J. Pitman and M. Yor) Math review 91h:31003 Curvature of the convex hull of planar Brownian motion near its minimum point. Stoch. Proc. Their Appl. 33, 1989, 89-103 (with J. San Martin). Math review 91e:60233 On Brownian excursions in Lipschitz domains. Part II. Local asymptotic distributions, Seminar on Stochastic Processes 1988 (E. Cinlar, K.L. Chung, R. Getoor, J. Glover, editors), 1989, 55-85, Birkhäuser, Boston. (with E. Toby and R.J. Williams) Math review 90k:60142 Percolation dimension of fractals, J. Math. Anal. Appl. 145, 1990, 282-288 Math review 90m:28007 Cut points on Brownian paths, Ann. Probab. 17, 1989, 1012-1036 Math review 90m:60091 Harmonic measure on 3-dimensional Brownian paths. Math. Proc. Cambridge Phil. Soc. 104, 1988, 407-412 Math review 89i:60084 Geometric properties of 2-dimensional Brownian paths. Probability Theory and Related Fields 81, 1989, 485-505 Math review 90g:60077 Minimal fine derivatives and Brownian excursions Nagoya Math. J. 119, 1990, 115-132 Math review 92b:60067 Some asymptotic laws for crossings and excursions. Colloque Paul Lévy sur les processus stochastiques. Asterisque 157-158, 59-74, Paris 1988 (with J.W. Pitman and M. Yor) Math review 90h:60070 On Brownian paths connecting boundary points. Ann. Probab. 16, 1988, 1034-1038 Math review 89f:60086 Remarks on angular derivative. Bull. Polish Acad. Sc. 34, 1986, 647-652 Math review 88d:30035 Convergence of 2-dimensional h-processes. Probab. Math. Statist. 8, 1987, 49-52 Math review 89c:60094 On Brownian excursions in Lipschitz domains, I. Local path properties. Trans. Amer. Math. Soc. 298, 1986, 289-306 (with R.J. Williams) Math review 88g:60183 Brownian excursions and minimal thinness, III. Applications to the angular derivative problem. Math. Z. 192, 1986, 89-107 Math review 89b:60175 Brownian excursions and minimal thinness, II. Applications to boundary behavior of the Green function. Seminar on Stochastic Processes 1985 (E. Cinlar, K.L. Chung, R.K. Getoor, eds.) 35-62 Birkhäuser, Boston Math review 88h:60150 Brownian excursions and minimal thinness, I. Ann. Probab. 15, 1987, 676-689 Math review 88h:60149 Brownian excursions from hyperplanes and smooth surfaces. Trans. Amer. Math. Soc. 295, 1986, 35-57 Math review 87j:60118 On a theorem of Salisbury. Probab. Math. Statist. 6, 1985, 161-166 Math review 88f:60130 Brownian paths and cones. Ann. Probab. 13, 1985, 1006-1010 Math review 86j:60183 The reproducibility property of fuzzy control systems. J. Fuzzy Sets and Systems 9, 1983, 161-177 (with J. Kiszka) Math review 84d:93020 On the non-existence of a selector of the maximal measure. Bull. Polish Acad. Sc. 29, 1981, 121-122 Math review 84h:28002 Certain ways of sequential classification. Przeglad Statystyczny 27, 1980, 131-147 (in Polish, with J. Burdzy) On equivalence of the induction principle and the maximum principle. Bull. Lublin Sc. Soc., 1976 (in Polish, with J. Burdzy) Other publications Mathematical articles and bottled water Notices AMS 49, May 2002, No. 5, p. 541, (online version) Introduction to the ejpecp class (package for a LaTeX2e class, online version) 2011 (with D. Chafai) On a book "Philosophy of Chance" by Michal Heller. Mathematica Applicanda 41 (2013) 225-247.