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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...
We define a new diffusive matrix model converging towards the $\beta$-Dyson Brownian motion for all $\beta\in [0,2]$ that provides an explicit construction of $\beta$-ensembles of random matrices that...
Real-world road networks have an approximate scale-invariance property; can one devise mathematical models of random networks whose distributions are {\em exactly} invariant under Euclidean scaling? T...
Abstract: We consider the asymptotics of the invariant measure for the process of the spatial distribution of $N$ coupled Markov chains in the limit of a large number of chains. Each chain reflects th...
Abstract: The uniqueness argument in the proof of Theorem 5, p. 483, of "Small noise asymptotics for invariant densities for a class of diffusions: a control theoretic view, J. Math. Anal. and Appl. (...
For biased random walk on the infinite cluster in supercritical i.i.d.percolation on Z2, where the bias of the walk is quantified by a parameter > 1,it has been conjectured (and partly proved) that ...
We study the invariant measure of a discretized stochastic Allen-Cahn equation in d+1 dimensions in the low noise limit. We consider a cuboidal domain and impose the two stable phases as boundary con...

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