•Journal•ISSN: 1083-589X
Electronic Communications in Probability
Institute of Mathematical Statistics
About: Electronic Communications in Probability is an academic journal published by Institute of Mathematical Statistics. The journal publishes majorly in the area(s): Random walk & Brownian motion. It has an ISSN identifier of 1083-589X. It is also open access. Over the lifetime, 1274 publications have been published receiving 19616 citations. The journal is also known as: ECP.
Topics: Random walk, Brownian motion, Fractional Brownian motion, Martingale (probability theory), Central limit theorem
Papers published on a yearly basis
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TL;DR: In this paper, a modern proof of Hanson-Wright inequality for quadratic forms in sub-gaussian random variables is given, and a useful concentration inequality for sub-Gaussian random vectors is given.
Abstract: In this expository note, we give a modern proof of Hanson-Wright inequality for quadratic forms in sub-gaussian random variables.We deduce a useful concentration inequality for sub-gaussian random vectors.Two examples are given to illustrate these results: a concentration of distances between random vectors and subspaces, and a bound on the norms of products of random and deterministic matrices.
687 citations
TL;DR: An exponential probability tail inequality for positive semidefinite quadratic forms in a subgaussian random vector is proved, analogous to one that holds when the vector has independent Gaussian entries.
Abstract: This article proves an exponential probability tail inequality for positive semidefinite quadratic forms in a subgaussian random vector. The bound is analogous to one that holds when the vector has independent Gaussian entries.
413 citations
TL;DR: In this paper, it was shown that under certain conditions, a hybrid chain will "inherit" the geometric ergodicity of its constituent parts, i.e., it can be seen as a Markov chain.
Abstract: Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the so-called hybrid chains. We prove that under certain conditions, a hybrid chain will "inherit" the geometric ergodicity of its constituent parts.
376 citations
TL;DR: In this paper, a comprehensive study of percolation in a more general context than the usual $Z^d$ setting is proposed, with particular focus on Cayley graphs, almost transitive graphs, and planar graphs.
Abstract: A comprehensive study of percolation in a more general context than the usual $Z^d$ setting is proposed, with particular focus on Cayley graphs, almost transitive graphs, and planar graphs. Results concerning uniqueness of infinite clusters and inequalities for the critical value $p_c$ are given, and a simple planar example exhibiting uniqueness and non-uniqueness for different $p>p_c$ is analyzed. Numerous varied conjectures and problems are proposed, with the hope of setting goals for future research in percolation theory.
296 citations
TL;DR: It is derived that concentration inequalities for functions of the empirical measure of eigenvalues for large, random, self adjoint matrices, with not necessarily Gaussian entries, are derived.
Abstract: We derive concentration inequalities for functions of the empirical measure of eigenvalues for large, random, self adjoint matrices, with not necessarily Gaussian entries. The results presented apply in particular to non-Gaussian Wigner and Wishart matrices. We also provide concentration bounds for non commutative functionals of random matrices.
266 citations