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Foundations of Computational Mathematics, ISSN 1615-3375, 8/2012, Volume 12, Issue 4, pp. 389 - 434
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 04/2020, Volume 101, Issue 2, pp. 682 - 713
We derive a functional central limit theorem for the excursion of a random walk conditioned on enclosing a prescribed geometric area. We assume that the... 
82B41 (secondary) | 60J10 (primary) | 60G50 | MATHEMATICS
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 04/2018, Volume 116, Issue 4, pp. 847 - 877
We study graph‐theoretic properties of the trace of a random walk on a random graph. We show that for any ε>0 there exists C>1 such that the trace of the... 
05C81 (primary) | 05C45 | 60G50 (secondary) | 05C80 | MATHEMATICS | COVER TIME
Journal Article
Probability Surveys, ISSN 1549-5787, 2007, Volume 4, Issue 1, pp. 1 - 79
Probability Surveys 2007, Vol. 4, 1-79 The models surveyed include generalized P\'{o}lya urns, reinforced random walks, interacting urn models, and continuous... 
Reinforced random walk | Urn model | Ṕolya's urn | VRRW | Dynamical system | Stochas-tic approximation | Self-avoiding walk | Agent-based model | Learning | Urn scheme | ERRW | Evo-lutionary game theory | Exchangeability | Lyapunov function | Mathematics - Probability
Journal Article
Journal of Statistical Physics, ISSN 0022-4715, 4/2016, Volume 163, Issue 1, pp. 22 - 40
We consider a generalization of a one-dimensional stochastic process known in the physical literature as Lévy-Lorentz gas. The process describes the motion of... 
Theoretical, Mathematical and Computational Physics | 60F05 (82C41, 60G55) | 60G50 | Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Random walks on point processes | Physics | Levy-Lorentz gas | Levy environment | Central Limit theorem | Physical Chemistry | Convergence of moments | Levy walks | RWRE
Journal Article
Journal of Mathematical Sciences (United States), ISSN 1072-3374, 04/2015, Volume 206, Issue 2, pp. 146 - 158
Zapiski Nauchnykh Seminarov POMI, 2013, vol. 420, p. 50-69, English translation in: J. Math. Sci. (N. Y.), 206:2 (2015), 146-158 Let $X,X_1,...,X_n$ be... 
Mathematics - Probability
Journal Article
Journal of applied probability, ISSN 0021-9002, 09/2015, Volume 52, Issue 3, pp. 752 - 770
We take a fresh look at the classical problem of runs in a sequence of independent and identically distributed coin tosses and derive a general... 
Research Papers | Regeneration | 60F99 | 60E10 | 60G40 | Poisson approximation | 60G50 | coin tossing | longest run | Laplace transform | Rouché's theorem | runs
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 04/2016, Volume 343, Issue 1, pp. 129 - 164
We define the model of two-dimensional random interlacements using simple random walk trajectories conditioned on never hitting the origin, and then obtain... 
COVER TIMES | DISCRETE TORUS | PHYSICS, MATHEMATICAL | PERCOLATION | 2 DIMENSIONS | Mathematics - Probability | Probability | Mathematics
Journal Article
Geometric and Functional Analysis, ISSN 1016-443X, 7/2017, Volume 27, Issue 4, pp. 880 - 918
Journal Article
The Annals of Applied Probability, ISSN 1050-5164, 12/2009, Volume 19, Issue 6, pp. 2047 - 2079
Journal Article
The Annals of Probability, ISSN 0091-1798, 9/2008, Volume 36, Issue 5, pp. 1946 - 1991
For a given one-dimensional random walk $\{S_{n}\}$ with a subexponential step-size distribution, we present a unifying theory to study the sequences... 
Mathematical theorems | Infinity | Clines | Random walk | Probability theory | Heuristics | Random variables | Truncation | Perceptron convergence procedure | Large deviations | Subexponentiality | large deviations | random walk | LIMIT-THEOREMS | BEHAVIOR | subexponentiality | STATISTICS & PROBABILITY | RANDOM-VARIABLES | SUMS | PROBABILITIES | Mathematics - Probability | 60F10 | 60G50
Journal Article
Journal of Statistical Physics, ISSN 0022-4715, 7/2015, Volume 160, Issue 2, pp. 321 - 335
Journal Article
The Annals of Probability, ISSN 0091-1798, 5/2009, Volume 37, Issue 3, pp. 1044 - 1079
Journal Article
Journal Article
Canadian journal of mathematics, ISSN 0008-414X, 10/2012, Volume 64, Issue 5, pp. 961 - 990
We study the densities of uniform random walks in the plane. A special focus is on the case of short walks with three or four steps and, less completely, those... 
Award Winners | Hypergeometric functions | Random walks | Mahler measure | INTEGRALS | MATHEMATICS | random walks | hypergeometric functions | ASYMPTOTICS | MAHLER MEASURES | INSTABILITY ZONES
Journal Article
Electronic Communications in Probability, ISSN 1083-589X, 2016, Volume 21
In this note we first consider local times of random walks killed at leaving positive half-axis. We prove that the distribution of the properly rescaled local... 
Second Ray-Knight theorem | Local time | Random walk | random walk | STATISTICS & PROBABILITY | second Ray-Knight theorem | local time
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 02/2019, Volume 99, Issue 1, pp. 97 - 126
We prove the noncommutative Davis decomposition for the column Hardy space Hpc for every 0 46L52 | 60G50 (secondary) | 60G42 (primary) | 46L53 | INTERPOLATION | MATHEMATICS | INEQUALITIES | SPACES
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 9/2012, Volume 25, Issue 3, pp. 703 - 732
For a branching process in random environment, it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from... 
Branching process | Random environment | Random walk | 60J80 | 60G50 | Probability Theory and Stochastic Processes | Functional limit theorem | Mathematics | Survival probability | Statistics, general | 60F17 | Change of measure | RANDOM-WALKS | STATISTICS & PROBABILITY | Mathematics - Probability
Journal Article
Experimental Mathematics, ISSN 1058-6458, 01/2018, Volume 27, Issue 1, pp. 100 - 110
The Collatz conjecture (also known as the 3x + 1 problem) concerns the behavior of the discrete dynamical system on the positive integers defined by iteration... 
Secondary 60G40, 60G50, 11Y99 | random walk | 3 x + 1 | Primary 11B83 | Collatz conjecture | discrete dynamical system
Journal Article
Annales de l'institut Henri Poincare (B) Probability and Statistics, ISSN 0246-0203, 02/2014, Volume 50, Issue 1, pp. 15 - 27
Journal Article
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