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What do card shuffling, volume growth, and Harnack inequalities have to do with each other? They all arise in the study of random walks on groups. Probability on groups is concerned with probabil...
Despite a true antipathy to the subject Hardy contributed deeply to modern probability. His work with Ramanujan begat probabilistic number theory. His work on Tauberian theorems and divergent series h...
We present an algorithm to store binary memories in a Hopfield neural network using minimum probability flow, a recent technique to fit parameters in energy-based probabilistic models. In the case of ...
Distributed consensus and other linear systems with system stochastic matrices $W_k$ emerge in various settings, like opinion formation in social networks, rendezvous of robots, and distributed infere...
Abstract: In this note, we compute the probability that a $k\times n$ matrix can be extended to an $n\times n$ invertible matrix over $\F_q[x]$, which turns out to be $(1-q^{k-n})(1-q^{k-1-n})...(1-q^...
Abstract: Hoeffding has shown that tail bounds on the distribution for sampling from a finite population with replacement also apply to the corresponding cases of sampling without replacement. (A spec...
The Dirac chord method may be suitable in different areas of physics for the repre-sentation of certain six-dimensional integrals for a convex body using the probability density of the chord length di...
Many applications in the eld of statistics require Markov chain Monte Carlo methods. Determining appropriate starting values and run lengths can be both analytically and empirically challenging.
Let μ be a probability measure on the real line. In this paper we prove that there exists a decomposition μ = μ0 ⊞μ1 ⊞· · ·⊞μn ⊞· · · such that μ0 is infinitely divisible and μ...
A Maple package HISTABRUT (available from ttp://www.math.rutgers.edu/~zeilberg/tokhniot/HISTABRUT)is presented and briefly described. It uses the polynomial ansatz to discover (often fully rigorously,...
We find the minimum probability of lifetime ruin of an investor who can invest in a market with a risky and a riskless asset and who can purchase a reversible life annuity. The surrender charge of a l...
We prove that the convolution of a selfdecomposable dis-tribution with its background driving law is again selfdecomposable if and only if the background driving law is s-selfdecomposable.

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