Related papers: Harry Kesten's work in probability theory
I review the classical theory of likelihood based inference and consider how it is being extended and developed for use in complex models and sampling schemes.
In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.
In this article, we merge celebrated results of Kesten and Spitzer [Z. Wahrsch. Verw. Gebiete 50 (1979) 5-25] and Kawazu and Kesten [J. Stat. Phys. 37 (1984) 561-575]. A random walk performs a motion in an i.i.d. environment and observes an…
This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related both to applications and to a modern…
This is a (long) survey about applications of percolation theory in equilibrium statistical mechanics. The chapters are as follows: 1. Introduction 2. Equilibrium phases 3. Some models 4. Coupling and stochastic domination 5. Percolation 6.…
The paper is devoted to the contribution in the Probability Theory of the well-known Soviet mathematician Alexander Yakovlevich Khintchine (1894-1959). Several of his results are described, in particular those fundamental results on the…
Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…
The asymptotic behavior of the tail probabilities for the first hitting times of the Bessel process with arbitrary index is shown without using the explicit expressions for the distribution function obtained in the authors' previous works.
Last three years have seen new developments in the theory of last passage percolation, which has variety applications to random permutations, random growth and random vicious walks. It turns out that a few class of models have determinant…
We consider the first hitting times of the Bessel processes. We give explicit expressions for the distribution functions and for the densities by means of the zeros of the Bessel functions. The results extend the classical ones and cover…
I am presenting a first-ever scientific collection of short sayings on probability and statistics expressed by most various men of science, many classics included, from antiquity to Kepler to our time. Quite understandably, the reader will…
We study branching processes in an i.i.d. random environment, where the associated random walk is of the oscillating type. This class of processes generalizes the classical notion of criticality. The main properties of such branching…
We study several constructions of the STIT tessellation process in a window of $\RR^\ell$ and supply an exact formula for its transition probability.
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
This expository paper features a few highlights of Richard Stanley's extensive work in Ehrhart theory, the study of integer-point enumeration in rational polyhedra. We include results from the recent literature building on Stanley's work,…
We consider the probability theory, and in particular the moment problem and universality theorems, for random groups of the sort of that arise or are conjectured to arise in number theory, and in related situations in topology and…
In this note, we try to analyze and clarify the intriguing interplay between some counting problems related to specific thermalized weighted graphs and random walks consistent with such graphs.
We correct a simple error in Percolation on random Johnson-Mehl tessellations and related models, Probability Theory and Related Fields 140 (2008), 417-468. (See also arXiv:math/0610716)
We define a new stochastic process on general simplicial complexes which allows to study their spectral and homological properties. Some results for random walks on graphs are shown to hold in this general setting. As an application, the…
The aim of this paper is to analyze a class of random motions which models the motion of a particle on the real line with random velocity and subject to the action of the friction. The speed randomly changes when a Poissonian event occurs.…