Large deviations and strong mixing
Aging for interacting diffusion processes
Persistence of iterated partial sums
Let denote the iterated partial sums. That is, , where . Assuming are integrable, zero-mean, i.i.d. random variables, we show that the persistence probabilities with (and whenever is symmetric). The converse inequality holds whenever the non-zero is bounded or when it has only finite third moment and in addition is squared integrable. Furthermore, for any non-degenerate squared integrable, i.i.d., zero-mean . In contrast, we show that for any there exist integrable, zero-mean...
Large deviations of Markov chains indexed by random trees
Markovian perturbation, response and fluctuation dissipation theorem
We consider the Fluctuation Dissipation Theorem (FDT) of statistical physics from a mathematical perspective. We formalize the concept of “linear response function” in the general framework of Markov processes. We show that for processes out of equilibrium it depends not only on the given Markov process () but also on the chosen perturbation of it. We characterize the set of all possible response functions for a given Markov process and show that at equilibrium they all satisfy the FDT. That is,...
Moderate deviations for martingales with bounded jumps.
Thin points for brownian motion
Transportation approach to some concentration inequalities in product spaces.
Large and moderate deviations for Hotelling's -statistic.
Brownian motion on compact manifolds: cover time and late points.
Thick points for transient symmetric stable processes.
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