相关论文: Harry Kesten's work in probability theory
The mathematical achievements of Harry Kesten since the mid-1950s have revolutionized probability theory as a subject in its own right and in its associations with aspects of algebra, analysis, geometry, and statistical physics. Through his…
In the introduction to this volume, we discuss some of the highlights of the research career of Chuck Newman. This introduction is divided into two main sections, the first covering Chuck's work in statistical mechanics and the second his…
The aims of this paper are twofold. Firstly, we derive some probabilistic representation for the constant which appears in the one-dimensional case of Kesten's renewal theorem. Secondly, we estimate the tail of some related random variable…
T. E. Harris was a pioneer par excellence in many fields of probability theory. In this paper, we give a brief survey of the many fundamental contributions of Harris to the theory of branching processes, starting with his doctoral work at…
Interacting particle systems and percolation have been among the most active areas of probability theory over the past half century. Ted Harris played an important role in the early development of both fields. This paper is a bird's eye…
This celebratory article contains a personal and idiosyncratic selection of a few open problems in discrete probability theory. These include certain well known questions concerning Lorentz scatterers and self-avoiding walks, and also some…
This text is a survey of the general theory of stochastic processes, with a view towards random times and enlargements of filtrations. The first five chapters present standard materials, which were developed by the French probability school…
Random walk is an explainable approach for modeling natural processes at the molecular level. The Random Permutation Set Theory (RPST) serves as a framework for uncertainty reasoning, extending the applicability of Dempster-Shafer Theory.…
There has been quite some activity and progress concerning spectral asymptotics of random operators that are defined on percolation subgraphs of different types of graphs. In this short survey we record some of these results and explain the…
We provide a new derivation of the well-known generating function counting the number of walks on a regular tree that start and end at the same vertex, and more generally, a generating function for the number of walks that end at a vertex a…
This article examines a recent body of work on stochastic processes indexed by a tree. Emphasis is on the application of this new framework to existing probability models. Proofs are largely omitted, with references provided.
We introduce and summarise results from the recent paper 'Biased random walk on the trace of biased random walk on the trace of ...', which was written jointly with M. P. Holmes (University of Melbourne). We also present additional…
We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a…
We analyze a class of continuous time random walks in $\mathbb R^d,d\geq 2,$ with uniformly distributed directions. The steps performed by these processes are distributed according to a generalized Dirichlet law. Given the number of changes…
This is an introduction to some of the most probabilistic aspects of free probability theory.
Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the `quenched' and the `averaged' case.
Let $S_n$ be the simple random walk on the integer lattice $\mathbb{Z}^d$. For a Bernstein function $\phi$ we consider a random walk $S^\phi_n$ which is subordinated to $S_n$. Under a certain assumption on the behaviour of $\phi$ at zero we…
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications.
In celebration of Professor Ron Doney's 80th birthday, we provide a summary of his academic career and contributions to probability theory, as one of the UK's leading probabilists for over 50 years. A version of this note also serves as an…