Markov loops ensembles

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Any semigroup of Markovian transition kernels defines a sigma-finite measure on loops which generates an increasing family of Poissonian loop ensembles. One can establish fundamental relations between these ensembles and several types of stochastic processes: Occupation fields, Gaussian free fields and their Wick powers, determinantal processes, branching forests, conformal loop ensembles and coalescence processes.

Лекция прочитана в рамках St. Petersburg School in Probability and Statistical Physics.

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