The following is a division of my published and submitted research papers according to their primary objectives. For a more traditional enumeration, please see the CV.
All preprints are downloadable from the Math arXiv.
Intertwining and hyperbolic equations
1. Interwined diffusions and wave equations.
- (with M. Shkolnikov) - Submitted.
Information geometry in mathematical finance
1. Energy, entropy, and Arbitrage.
- (with Leonard Wong) - Submitted.
Rank-based models: shape and stability of market weights
1. One dimensional Brownian particle systems with rank-dependent drifts.
- (with J. Pitman) - Annals of Applied Probability, 18(6), 2179--2207, 2008.
2. A phase transition behavior for Brownian motions interacting through their ranks
- (with S. Chatterjee) - PTRF, 147(1-2), 123--159, 2010.
3. Concentration of measure for systems of Brownian particles interacting through their ranks - (with M. Shkolnikov). To appear in The Annals of Applied Probability.
4. Convergence rates of rank-based processes with applications to portfolio theory - (with T. Ichiba and M. Shkolnikov). To appear in PTRF.
5. Systems of Brownian particles with asymmetric collisions - (with I. Karatzas and M. Shkolnikov). Submitted.
Edge of universality: spectral properties of sparse random regular graphs
1. Sparse random regular graphs: spectral density and eigenvectors.
- (with I. Dumitriu) -The Annals of Probability 40(5), 2197--2235, 2012.
2. Functional limit theorems for random regular graphs.
- (with I. Dumitriu, T. Johnson, E. Paquette) - PTRF 156(3-4), 921--975, 2013.
3. Cycles and eigenvalues of sequentially growing random regular graphs.
- (with T. Johnson) - To appear in The Annals of Probability.
Transport and concentration inequalities for stochastic processes
1. Concentration for multidimensional diffusions and their boundary local time.
- PTRF 154 (1), 225--254, 2012.
Stochastic processes related to combinatorics
1. On the Aldous diffusion on continuum trees. I.
- Preprint.
2. Wright-Fisher models with negative mutation rates.
- The Annals of Probability 41(2) 503-526, 2013.
3. A combinatorial analysis of interacting diffusions.
- (with S. Chatterjee). To appear in Journal of Theoretical Probability.
4. Brownian approximation to counting graphs.
- To appear in SIDMA.
4. On meteors, earthworms and WIMPs.
-(with K. Burdzy, S. Billey, and B. Sagan) Submitted.
Miscellaneous articles on continuous stochastic processes
- (with K. Burdzy and Z.-Q. Chen ). To appear in The Annals of Probability.
2. Crowding of Brownian spheres.
- (with K. Burdzy and J. Swanson). ALEA 7(2010) 193-205.
3. Markov processes on time-like graphs.
- (with Chris Burdzy). To appear in The Annals of Probability.
4. Archimedes' principle for Brownian liquid.
- (with K. Burdzy and Z.-Q. Chen). To appear in The Annals of Applied Probability.
5. Extinction of Fleming-Viot-type particle systems with strong drift.
- (with K. Burdzy and M. Bieniek). EJP.
Miscellaneous articles on math finance
1. Analysis of the market weights under the volatility-stabilized market models.
- The Annals of Applied Probability 21(3), 1180--1213, 2011.
2. Analysis of continuous strict local martingales via h-transforms.
- (with P. Protter). SPA, 120 (8) 1424--1443, 2010.
3. Computing strategies for achieving acceptability: a Monte-Carlo approach.
- SPA, 117, 2179--2207, 2007.
Others
1. An excursion-theoretic approach to the stability of discrete time stochastic hybrid systems. - (with D. Chatterjee). AMO, 63 (2) 217 -- 237, 2011.
2. Symmetrization of Bernoulli.
- Electronic Communications in Probability, 13, 194--197, 2008.