Stationary measures for random walks in a random environment with random scenery.
Processes on unimodular random networks.
Determinantal probability measures
Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We study basic combinatorial and probabilistic aspects in the discrete case. Our main results concern relationships with matroids, stochastic domination, negative association, completeness for infinite matroids, tail triviality, and a method for extension of results from orthogonal projections to positive contractions. We also present several new avenues for further investigation,...
La mesure des ensembles non-normaux.
The measure of non-normal sets.
The size of some classes of thin sets
Topologies on measure spaces and the Radon-Nikodym theorem
Ends in uniform spanning forests.
Markov chain intersections and the loop-erased walk
Random orderings and unique ergodicity of automorphism groups
We show that the only random orderings of finite graphs that are invariant under isomorphism and induced subgraph are the uniform random orderings. We show how this implies the unique ergodicity of the automorphism group of the random graph. We give similar theorems for other structures, including, for example, metric spaces. These give the first examples of uniquely ergodic groups, other than compact groups and extremely amenable groups, after Glasner andWeiss’s example of the group of all permutations...
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