

Publications
Books

Brownian Motion and its Applications to Mathematical Analysis.
École d'Été de Probabilités de SaintFlour 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
 Stirring two grains of sand (preprint)
(Math ArXiv version)
 A Lorentz model with variable density in a gravitational field: limit theorems and recurrence
(preprint, with D. Rizzolo)
(Math ArXiv version)

Meteor process on ${\mathbb Z}^d$
(preprint)
(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.
(to appear, with S. Billey, S. Pal and B. Sagan)
(Math ArXiv version)
 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 (preprint, with M. Barlow and A. Timar)
(Math ArXiv version)

Forward Brownian motion
Probab. Theory Rel. Fields 160 (2014) 95126
(with M. Scheutzow)

Joint convergence along different subsequences of the signed cubic
variation of fractional Brownian motion
Probab. Theory Rel. Fields 159 (2014) 237272
(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.
(to appear,
with M. Bramson and W. Kendall)
(Math ArXiv version)
 Invisibility via reflecting coating
J. London Math. Soc.
(to appear,
with T. Kulczycki)
(Math ArXiv version)
 Deterministic approximations of random reflectors
Trans. Amer. Math. Soc. 365 (2013) 63676383
(with O. Angel and S. Sheffield)
 Extinction of FlemingViottype particle systems with strong drift
Electron. J. Probab. 17 (2012), paper 11, 115
(with M. Bieniek and S. Pal)
 Reflecting random walk in fractal domains
Ann. Probab. 41 (2013) 27912819
(with Z. Chen)
 Brownian earthworm
Ann. Probab. 41 (2013) 40024049
(with Z. Chen and S. Pal)
 Isolated zeros for Brownian motion with variable drift
Electron. J. Probab. 16 (2011), paper 65, 17931815
(with T. Antunovic, Y. Peres and J. Ruscher)
 Stationary distributions for jump processes with memory
Ann. I. H. Poincaré
48 (2012) 609630
(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, 139172
(with T. Kulczycki and R. Schilling)
 Nonuniqueness for nonnegative solutions of parabolic
stochastic partial differential equations
Illinois J. Math.,
Burkholder Volume
54 (2010) 14811507
(with C. Mueller and
E. Perkins)
 Shy Couplings, CAT(0) Spaces, and the Lion and Man
Ann. Probab.
41 (2013) 744784
(with M. Bramson and W. Kendall)
 Comment on article by Robert Bayesian Analysis
5 (2010) 233236.
 Crowding of Brownian spheres
ALEA Lat. Am. J. Probab. Math. Stat.
7 (2010) 193205 (with
S. Pal and J. Swanson)
 Archimedes' principle for Brownian liquid
Ann. Appl. Probab.
21 (2011) 20532074
(with Z. Chen and S. Pal)
 Markov processes on timelike graphs
Ann. Probab. 39 (2011) 13321364
(with S. Pal)
 Nonextinction of a FlemingViot particle model
Probab. Theory Rel. Fields 153
(2012) 293332
(with
M. Bieniek and S. Finch)
 Differentiability of stochastic flow of reflected
Brownian motions
Electron. J. Probab. 14 (2009) 21822240.
 Multiplicative functional for reflected Brownian
motion via deterministic ODE
Illinois J. Math.,
Burkholder Volume, 54 (2010) 895925
(with J. Lee)
 Stationary distributions for diffusions with inert
drift
Probab. Theory Rel. Fields 146 (2010) 147
(with R. Bass, Z. Chen and M. Hairer)
 A change of variable formula with Ito correction term
Ann. Probab. 38 (2010) 18171869
(with J. Swanson)
 The Skorokhod problem in a timedependent interval
Stoch. Process. Appl. 119 (2009) 428452
(with W. Kang and K. Ramanan)
 Markov processes with productform stationary distribution
Electron. Comm. Probab. 13 (2008) 614627
(with D. White)
 On pathwise uniqueness for reflecting Brownian motion
in $C^{1+\gamma}$ domains
Ann. Probab. 36 (2008) 23112331
(with R. Bass)
 Brownian motion with inert drift, but without flux: a
model
Physica A 384 (2007) 278284
(with R. Holyst and L. Pruski)
 Discrete approximations to reflected Brownian motion
Ann. Probab. 36, (2008) 698727
(with Z. Chen)
 Mirror couplings and Neumann eigenfunctions
Indiana U. Math. J. 57 (2008) 13171353.
(with R. Atar)
 Pathwise uniqueness for a degenerate stochastic
differential equation
Ann. Probab. 35, (2007) 23852418
(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 178181.
(with R. Bass)
 Shy couplings
Probab. Theory Rel. Fields 137 (2007) 345377.
(with I. Benjamini and Z. Chen)
 Comparison of potential theoretic properties of rough
domains Proc. AMS 134 (2006), 32473253.
 On the Robin problem in fractal domains
Proc. London Math. Soc. 96 (2008), 273311
(with R. Bass and Z. Chen)
 An annihilatingbranching particle model for the heat
equation with average temperature zero
Ann. Probab. 34, (2006) 23822405
(with J. Quastel)
 Synchronous couplings of reflected Brownian motions in
smooth domains Illinois J. Math., Doob Volume
50 (2006) 189268
(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. 1123
(review paper)
 A Gaussian oscillator Electron. Comm. Probab. 9
(2004), paper 10, pp. 9295 (with D. White)
 The "hot spots" problem in planar domains with one
hole. Duke Math. J. 129 (2005) 481502

The heat equation in time dependent domains with
insulated boundaries J. Math. Anal. Appl. 294 (2004)
581595
(with Z. Chen and J. Sylvester)
 Coalescence on the highdimensional sphere: a
caricature for perfect simulation. Symposium in Honour of Ole
E. BarndorffNielsen (Aarhus, 2000), 5052, Memoirs, 16, Univ.
Aarhus, Aarhus, 2000 (with W. Kendall)
 Traps for reflected Brownian motion
Math. Z. 252 (2006) 103132
(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) 134
(with Z. Chen and J. Sylvester)
 Lenses in skew Brownian flow
Ann. Probab. 32 (2004) 30853115
(with H. Kaspi)
 Stochastic differential equations driven by stable
processes for which pathwise uniqueness fails
Stoch. Proc. and their Appl. 111 (2004) 115
(with R. Bass and Z. Chen)
 Erratum to "The supremum of Brownian local times on Hölder curves"
Ann. I. H. Poincaré 38 (2002) 799800 (with
R. Bass)
 SuperBrownian motion with reflecting historical
paths. II. Convergence of approximations
Probab. Theory Rel. Fields 133 (2005) 145174
(with L. Mytnik)
 Uniqueness for reflecting Brownian motion in lip domains
Ann. I. H. Poincaré 41 (2005) 197235
(with R. Bass and Z. Chen)
 On nodal lines of Neumann eigenfunctions
Electron. Comm. Probab. 7, (2002)
paper 14, p. 129139
(with R. Atar)
 On Neumann eigenfunctions in lip domains
Journal AMS 17 (2004) 243265
(with R. Atar)
 Shocks and business cycles Advances in Theoretical
Economics 5 (2005) 186, no. 1, article 2
(with D. Frankel)
 Censored stable processes
Probab. Theory Rel. Fields 127 (2003) 89152
(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) 553578
(with Z. Chen)
 Stable processes have thorns
Ann. Probab. 31 (2003) 170194
(with T. Kulczycki)
 Brownian motion reflected on Brownian motion
Probab. Theory Rel. Fields 122 (2002) 471493
(with D. Nualart)
 The heat equation and reflected Brownian motion
in time dependent domains
Ann. Probab.32 (2004) 775804
(with Z. Chen and J. Sylvester)
 SuperBrownian motion with reflecting historical paths
Probab. Theory Rel. Fields
121 (2001) 447491
(with J.F. Le Gall)
 The supremum of Brownian local times on Hölder curves
Ann. Inst. Henri Poincaré 37 (2001) 627642
(with R. Bass)
 Reduction of dimensionality in a diffusion
search process and kinetics of gene expression
Physica A, 277 (2000) 7182) (with R. Holyst,
M. Blazejczyk, G. Goralski and L. Bocquet)
 Coalescence of skew Brownian motions
Seminaire de Probabilites XXXV, LNM 1755
(2001) 202205
(with M. Barlow, H. Kaspi and A. Mandelbaum)
 A FlemingViot particle representation of Dirichlet Laplacian
Comm. Math. Phys. 214 (2000) 679703
(with R. Holyst and P. March)
 Diffusion on curved periodic surfaces
Phys. Rev. E 60 (1999) 302307
(with R. Holyst, D. Plewczynski
and A. Aksimentiev)
 Fiber Brownian motion and the `hot spots' problem
Duke Math. J. 105 (2000) 2558
(with R. Bass)
Math review 2001g:60190
 Local time flow related to skew Brownian motion
Ann. Probab. 29 (2001) 16931715
(with Z.Q. Chen)

Variably skewed Brownian motion
Electr. Comm. Probab. 5, (2000)
paper 6, p. 5766.
(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. 2933
(with Z.Q. Chen)
Math review 99d:60091
 Efficient Markovian couplings: examples and counterexamples
Ann. Appl. Probab. 10 (2000)
362409. (with W. Kendall)
 A counterexample to the "hot spots" conjecture
Ann. Math. 149 (1999) 309317
(with W. Werner)
Math review 2000b:35044
 Stochastic bifurcation models
Ann. Probab. 27 (1999) 50108
(with R. Bass)
Math review 2000b:60201
 On minimal parabolic functions and timehomogeneous
parabolic $h$transforms
Trans. Amer. Math. Soc. 351 (1999)
34993531
(with T. Salisbury)
Math review 99m:60113

Positivity of Brownian transition densities
Electr. Comm. Probab. 2 (1997)
paper 4, p. 4153
(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. 483500.
Elsevier, Amsterdam, 1998.
(with D. Frankel and A. Pauzner)
Math review 99k:60148
 Brownian motion in a Brownian crack
Ann. Appl. Probab. 8 (1998) 708748
(with D. Khoshnevisan)
Math review 99g:60147
 On the "hot spots" conjecture of J. Rauch
J. Func. Anal. 164 (1999) 133
(with R. Bañuelos)
Math review 2000m:35085
 Fast equilibrium selection by rational
players living in a changing world
Econometrica 69 (2001) 163190
(with D. Frankel and A. Pauzner)
 Sets avoided by Brownian motion
Ann. Probab. 26 (1998) 429464
(with O. Adelman and R. Pemantle)
Math review 99i:60152
 Configurational transition in a FlemingViottype model
and probabilistic interpretation of Laplacian eigenfunctions
J. Phys. A 29, 1996, 26332642.
(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,
119. (with R. Bass)
Math review 97c:60201
 A critical case for Brownian slow points
Probab. Th. Rel. Fields 105, 1996, 85108.
(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, 231236.
(with D. Khoshnevisan)
Math review 98k:60138
 No triple point of planar Brownian motion
is accessible Ann. Probab. 24, 1996, 125147
(with W. Werner)
Math review 97j:60147
 Ito formula for an asymptotically
4stable process Ann. Appl. Probab. 6,
1996, 200217 (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, 5669.
(with S. Attal, M. Émery and Y. Hu)
Math review 98j:60111
 Iterated law of iterated logarithm
Ann. Probab. 23, 1995, 16271643
(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, 165193.
Math review 97j:60146
 Conditioned Brownian motion in planar domains
Probab. Th. Rel. Fields 101, 1995, 479493
(with R. Bass)
Math review 96b:60199
 2D Brownian motion in a system of reflecting barriers:
effective diffusivity by a sampling method
J. Phys. A: Math. General 27, 1994, 631644.
(with R. Holyst and D. Ingerman)
 An asymptotically 4stable process
J. Fourier Anal. Appl. Special Issue.
Proceedings of the Conference in Honor of J.P. Kahane,
1995, 97117. (with A. Madrecki)
Math review 96j:60072
 A Skorohodtype lemma and a decomposition
of reflected Brownian motion Ann. Probab. 23,
1995, 586604 (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, 177181.
Math review 95m:60118
 Variation of iterated Brownian motion.
MeasureValued
Processes, Stochastic Partial Differential Equations
and Interacting Systems, D.A. Dawson, ed.,
CRM Proceedings and Lecture Notes
5, 1994, 3553.
Math review 95h:60123
 On domain monotonicity of the Neumann heat
kernel. J. Func. Anal. 116, 1993, 215224
(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, 6787.
Math review 95c:60075
 Intersection local time for points of infinite multiplicity.
Ann. Probab. 22, 1994, 566625
(with R. Bass and D. Khoshnevisan)
Math review 95j:60118
 A threedimensional Brownian path reflected
on a Brownian path is a free Brownian path.
Letters Math. Phys. 27, 1993, 239241
Math review 94c:60132
 2D Brownian motion in a system of traps:
Application of conformal transformations.
J. Phys. A: Math. General 25, 1992, 24632471
(with R. Holyst and T. Salisbury)
 The boundary Harnack principle for nondivergence form
elliptic operators. J. London Math. Soc. 50, 1994, 157169
(with R. Bass)
Math review 95f:35058
 Nonpolar points for reflected Brownian motion.
Ann. Inst. Henri Poincaré 29, 1993, 199228
(with D. Marshall)
Math review 94g:60152
 The Martin boundary in nonLipschitz domains.
Trans. Amer. Math. Soc. 337, 1993, 361378
(with R. Bass)
Math review 93g:31019
 Hölder domains and the boundary Harnack principle.
Duke Math. J. 64, 1991, 195200
(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, 8194. (with D. Marshall)
Math review 94g:60151
 Lifetimes of conditioned diffusions.
Probab. Th. Rel. Fields 91, 1992, 405443.
(with R. Bass)
Math review 93e:60155
 A boundary Harnack principle in twisted Hölder domains.
Ann. Math. 134, 1991, 253276 (with R. Bass)
Math review 92m:31006
 Rigorous exponent inequalities for random walks.
J. Phys. A: Math. Gen. 23, 1990, L23L28
(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, 116 (with R. Bass)
Math review 92c:60106
 A representation of local time for Lipschitz surfaces.
Probab. Th. Rel. Fields 84, 1990, 521547
(with R. Bañuelos and R. Bass)
Math review 91f:60139
 On nonincrease of Brownian motion. Ann. Probab.
18, 1990, 978980.
Math review 91e:60234
 Nonintersection exponents for Brownian paths. Part II.
Estimates and applications to a random fractal.
Ann. Probab. 18, 1990, 9811009.
(with G. Lawler)
Math review 91g:60097
 Nonintersection exponents for Brownian paths. Part I.
Existence and an invariance principle.
Probab. Th. Rel. Fields 84,
1990, 393410 (with G. Lawler)
Math review 91g:60096
 On the critical exponent for random walk intersections.
J. Stat. Phys. 56, 1989, 112
(with G. Lawler and T. Polaski)
Math review 91h:60073
 Brownian crossings between spheres,
J. Math. Anal. Appl. 148, 1990,
101120 (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, 89103
(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, 5585, Birkhäuser, Boston.
(with E. Toby and R.J. Williams)
Math review 90k:60142
 Percolation dimension of fractals,
J. Math. Anal. Appl. 145, 1990, 282288
Math review 90m:28007
 Cut points on Brownian paths, Ann. Probab. 17,
1989, 10121036
Math review 90m:60091
 Harmonic measure on 3dimensional Brownian paths.
Math. Proc. Cambridge Phil. Soc. 104, 1988, 407412
Math review 89i:60084
 Geometric properties of 2dimensional Brownian
paths. Probability Theory and Related Fields 81,
1989, 485505
Math review 90g:60077
 Minimal fine derivatives and Brownian excursions
Nagoya Math. J. 119, 1990, 115132
Math review 92b:60067
 Some asymptotic laws for crossings and excursions.
Colloque Paul Lévy sur les processus stochastiques.
Asterisque 157158, 5974, Paris 1988
(with J.W. Pitman and M. Yor)
Math review 90h:60070
 On Brownian paths connecting boundary
points. Ann. Probab. 16, 1988, 10341038
Math review 89f:60086
 Remarks on angular derivative.
Bull. Polish Acad. Sc. 34, 1986, 647652
Math review 88d:30035
 Convergence of 2dimensional hprocesses.
Probab. Math. Statist. 8, 1987, 4952
Math review 89c:60094
 On Brownian excursions in Lipschitz domains, I. Local path
properties. Trans. Amer. Math. Soc. 298,
1986, 289306 (with R.J. Williams)
Math review 88g:60183
 Brownian excursions and minimal thinness, III. Applications to the
angular derivative problem. Math. Z. 192,
1986, 89107
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.)
3562 Birkhäuser, Boston
Math review 88h:60150
 Brownian excursions and minimal thinness, I.
Ann. Probab. 15, 1987, 676689
Math review 88h:60149
 Brownian excursions from hyperplanes and smooth surfaces.
Trans. Amer. Math. Soc. 295, 1986, 3557
Math review 87j:60118
 On a theorem of Salisbury. Probab. Math.
Statist. 6, 1985, 161166
Math review 88f:60130
 Brownian paths and cones. Ann. Probab. 13,
1985, 10061010
Math review 86j:60183
 The reproducibility property of fuzzy control systems.
J. Fuzzy Sets and Systems 9, 1983, 161177 (with J. Kiszka)
Math review 84d:93020
 On the nonexistence of a selector of the maximal measure.
Bull. Polish Acad. Sc. 29, 1981, 121122
Math review 84h:28002
 Certain ways of sequential classification.
Przeglad Statystyczny 27, 1980, 131147 (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) 225247.

