Foundations of computational mathematics, ISSN 1615-3383, 2011, Volume 12, Issue 4, pp. 389 - 434

This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable...

Economics general | Random matrix | 60F10 | 60G42 | 60G50 | Linear and Multilinear Algebras, Matrix Theory | 60B20 | Mathematics | Large deviation | Numerical Analysis | Discrete-time martingale | Sum of independent random variables | Probability inequality | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | KHINTCHINE | MATHEMATICS, APPLIED | INEQUALITIES | CONVEXITY | MATHEMATICS | GAUSSIAN-PROCESSES | COMPUTER SCIENCE, THEORY & METHODS | ENTROPY | Probability | Algorithms | Eigenvalues | Mathematics - Probability

Economics general | Random matrix | 60F10 | 60G42 | 60G50 | Linear and Multilinear Algebras, Matrix Theory | 60B20 | Mathematics | Large deviation | Numerical Analysis | Discrete-time martingale | Sum of independent random variables | Probability inequality | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | KHINTCHINE | MATHEMATICS, APPLIED | INEQUALITIES | CONVEXITY | MATHEMATICS | GAUSSIAN-PROCESSES | COMPUTER SCIENCE, THEORY & METHODS | ENTROPY | Probability | Algorithms | Eigenvalues | Mathematics - Probability

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

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

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

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 applied probability, ISSN 0021-9002, 12/2007, Volume 44, Issue 4, pp. 889 - 900

Assume that there are k types of insurance contracts in an insurance company. The ith related claims are denoted by {X ij , j ≥ 1}, i = 1,…,k. In this paper we...

Research Papers | Sums of random variables | Loss process | Consistently varying tail | Large deviation | sums of random variables | 60F10 | consistently varying tail | 60G50 | loss process | 60F05

Research Papers | Sums of random variables | Loss process | Consistently varying tail | Large deviation | sums of random variables | 60F10 | consistently varying tail | 60G50 | loss process | 60F05

Journal Article

Journal of statistical physics, ISSN 1572-9613, 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

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 applied probability, ISSN 0021-9002, 09/2004, Volume 41, Issue 3, pp. 623 - 638

A continuous-time random walk is a simple random walk subordinated to a renewal process used in physics to model anomalous diffusion. In this paper we show...

Research Papers | Continuous-time random walk | Operator self-similar process | continuous-time random walk | 60K40 | 60G50

Research Papers | Continuous-time random walk | Operator self-similar process | continuous-time random walk | 60K40 | 60G50

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

Mathematics - Probability

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 06/2010, Volume 153, Issue 3, pp. 475 - 510

The cutoff phenomenon describes a sharp transition in the convergence of a family of ergodic finite Markov chains to equilibrium. Many natural families of...

MATHEMATICS | 60J10 | 60B10 | 05C80 | 60G50

MATHEMATICS | 60J10 | 60B10 | 05C80 | 60G50

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 08/2017, Volume 168, Issue 3-4, pp. 691 - 719

We study the boundary of the range of simple random walk on in the transient case . We show that volumes of the range and its boundary differ mainly by a...

60F05 | 60G50 | STATISTICS & PROBABILITY | Random walk | Random walk theory | Variance | Probability | Mathematics

60F05 | 60G50 | STATISTICS & PROBABILITY | Random walk | Random walk theory | Variance | Probability | Mathematics

Journal Article

The Annals of probability, ISSN 0091-1798, 2015, Volume 43, Issue 3, pp. 992 - 1044

We study the asymptotic behavior of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and...

Weyl chamber | Random walk | Harmonic function | Exit time | BROWNIAN-MOTION | WEYL CHAMBERS | exit time | STATISTICS & PROBABILITY | harmonic function | POTENTIAL-THEORY | SMALL STEPS | SUMS | CENTRAL LIMIT-THEOREMS | EXIT TIMES | STAY | Mathematics - Probability | 60G40 | 60G50 | 60F17

Weyl chamber | Random walk | Harmonic function | Exit time | BROWNIAN-MOTION | WEYL CHAMBERS | exit time | STATISTICS & PROBABILITY | harmonic function | POTENTIAL-THEORY | SMALL STEPS | SUMS | CENTRAL LIMIT-THEOREMS | EXIT TIMES | STAY | Mathematics - Probability | 60G40 | 60G50 | 60F17

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

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

COVER TIMES | DISCRETE TORUS | PHYSICS, MATHEMATICAL | PERCOLATION | 2 DIMENSIONS | Mathematics - Probability | Probability | Mathematics

Journal Article

Geometric and functional analysis, ISSN 1420-8970, 2017, Volume 27, Issue 4, pp. 880 - 918

We give an explicit formula for the probability that the convex hull of an n-step random walk in $${\mathbb{R}^d}$$ R d does not contain the origin, under the...

60D05 | Primary 52A22 | Characteristic polynomial | 52A23 | Distribution-free probability | Wendel’s formula | Mathematics | Hyperplane arrangement | Whitney’s formula | 60G09 | Zaslavsky’s theorem | Weyl chamber | Secondary 60G50 | Finite reflection group | Random walk | 52A55 | Conic intrinsic volume | 52C35 | Convex cone | Absorption probability | Convex hull | Mod-Poisson convergence | Analysis | Sparre Andersen’s Theorem | Random walk bridge | Exchangeability | 20F55 | Sparre Andersen's Theorem | Zaslavsky's theorem | MATHEMATICS | Whitney's formula | Wendel's formula

60D05 | Primary 52A22 | Characteristic polynomial | 52A23 | Distribution-free probability | Wendel’s formula | Mathematics | Hyperplane arrangement | Whitney’s formula | 60G09 | Zaslavsky’s theorem | Weyl chamber | Secondary 60G50 | Finite reflection group | Random walk | 52A55 | Conic intrinsic volume | 52C35 | Convex cone | Absorption probability | Convex hull | Mod-Poisson convergence | Analysis | Sparre Andersen’s Theorem | Random walk bridge | Exchangeability | 20F55 | Sparre Andersen's Theorem | Zaslavsky's theorem | MATHEMATICS | Whitney's formula | Wendel's formula

Journal Article

Journal of applied probability, ISSN 0021-9002, 09/2011, Volume 48, Issue 3, pp. 624 - 636

We study four discrete-time stochastic systems on N, modeling processes of rumor spreading. The involved individuals can either have an active or a passive...

Research Papers | Coverage of space | Rumor model | Epidemic model | Disk percolation | Mathematics - Probability | disk percolation | 60K35 | rumor model | epidemic model | 60G50

Research Papers | Coverage of space | Rumor model | Epidemic model | Disk percolation | Mathematics - Probability | disk percolation | 60K35 | rumor model | epidemic model | 60G50

Journal Article

The Annals of Applied Probability, ISSN 1050-5164, 12/2009, Volume 19, Issue 6, pp. 2047 - 2079

For the sum process X = X¹ + X² of a bivariate Lévy process (X¹, X²) with possibly dependent components, we derive a quintuple law describing the first upwards...

Fluctuation theorem | Copula functions | Investment risk | Random walk | Insurance risk | Coordinate systems | Business risks | Industrial sectors | Jumping | Probabilities | Dependence modeling | Fluctuation theory | Lévy copula | Ruin theory | Ladder process | Multivariate Lévy process | First passage event | ruin theory | RUIN PROBABILITIES | ladder process | multivariate Levy process | STATISTICS & PROBABILITY | fluctuation theory | Levy copula | dependence modeling | OVERSHOOTS | 60J75 | 60G51 | multivariate Lévy process | 60G50 | 91B30

Fluctuation theorem | Copula functions | Investment risk | Random walk | Insurance risk | Coordinate systems | Business risks | Industrial sectors | Jumping | Probabilities | Dependence modeling | Fluctuation theory | Lévy copula | Ruin theory | Ladder process | Multivariate Lévy process | First passage event | ruin theory | RUIN PROBABILITIES | ladder process | multivariate Levy process | STATISTICS & PROBABILITY | fluctuation theory | Levy copula | dependence modeling | OVERSHOOTS | 60J75 | 60G51 | multivariate Lévy process | 60G50 | 91B30

Journal Article

The Annals of probability, ISSN 0091-1798, 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

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

The Annals of Probability, ISSN 0091-1798, 5/2009, Volume 37, Issue 3, pp. 1044 - 1079

Given a branching random walk, let $M_{n}$ be the minimum position of any member of the nth generation. We calculate EMn to within O(1) and prove exponential...

Integers | Brownian motion | Rooting depth | Infinity | Conditional probabilities | Random walk | Random variables | Children | Mathematical minima | Vertices | Branching random walks | Random trees | Branching processes | POSITION | random trees | STATISTICS & PROBABILITY | WEIGHTED HEIGHT | DISPLACEMENT | BINARY SEARCH-TREES | branching processes | DEVIATIONS | Mobile Computing | Networking and Internet Architecture | Computer Science | 60J80 | 60G50

Integers | Brownian motion | Rooting depth | Infinity | Conditional probabilities | Random walk | Random variables | Children | Mathematical minima | Vertices | Branching random walks | Random trees | Branching processes | POSITION | random trees | STATISTICS & PROBABILITY | WEIGHTED HEIGHT | DISPLACEMENT | BINARY SEARCH-TREES | branching processes | DEVIATIONS | Mobile Computing | Networking and Internet Architecture | Computer Science | 60J80 | 60G50

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 7/2015, Volume 160, Issue 2, pp. 321 - 335

In this paper we obtain a couple of explicit expressions for the derivative of the probability of an increasing event in the random interlacements model. The...

Secondary 60G50 | Plus-pivotal trajectories | Primary 60K35 | Theoretical, Mathematical and Computational Physics | Russo’s formula | Quantum Physics | 82C41 | Statistical Physics, Dynamical Systems and Complexity | Physics | Increasing events | Physical Chemistry | Random interlacements | Percolation | Russo's formula | VACANT SET | PHYSICS, MATHEMATICAL | Mathematics - Probability

Secondary 60G50 | Plus-pivotal trajectories | Primary 60K35 | Theoretical, Mathematical and Computational Physics | Russo’s formula | Quantum Physics | 82C41 | Statistical Physics, Dynamical Systems and Complexity | Physics | Increasing events | Physical Chemistry | Random interlacements | Percolation | Russo's formula | VACANT SET | PHYSICS, MATHEMATICAL | Mathematics - Probability

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

Award Winners | Hypergeometric functions | Random walks | Mahler measure | INTEGRALS | MATHEMATICS | random walks | hypergeometric functions | ASYMPTOTICS | MAHLER MEASURES | INSTABILITY ZONES

Journal Article

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