In this paper we consider the field of local times of a discrete-time Markov chain on a general state space, and obtain uniform (in time) upper bounds on the total variation distance between this field and the one of a sequence of n i.i.d. random variables with law given by the invariant measure of that Markov chain. The proof of this result uses a refinement of the soft local time method of [11].

In this paper we obtain a couple of explicit expressions for the derivative of the probability of an increasing event in the random interlacements model. The event is supported in a finite subset of the lattice, and the derivative is with respect to the intensity parameter of the model.

In this paper we obtain a decoupling feature of the random interlacements process I u ⊂ Z d , at level u, d ≥ 3. More precisely, we show that the trace of the random interlacements process on two disjoint finite sets, F and its translated F + x, can be coupled with high probability of success, when x is large, with the trace of a process of independent excursions, which we call the noodle soup process. As a consequence, we obtain an upper bound on the covariance between two [0, 1]-valued functions depending on the configuration of the random interlacements on F and F + x, respectively. This improves a previous bound obtained by Sznitman in [9].

A new Bayesian measure of evidence is used for model choice within the generalized extreme value family of distributions, given an absolutely continuous posterior distribution on the related parametric space. This criterion allows quantitative measurement of evidence of any sharp hypothesis, with no need of a prior distribution assignment to it. We apply this methodology to the testing of the precise hypothesis given by the Gumbel model using real data. Performance is compared with usual evidence measures, such as Bayes factor, Bayesian information criterion, deviance information criterion and descriptive level for deviance statistic.

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