Título: Random walks in cooling random environments: a journey on the one-dimensional lattice

Palestrante: Luca Avena (Leiden University)
Data: 17/05/2021
Horário: 15:00h
Local: Transmissão online.

Confira AQUI o link para a transmissão.

Resumo: RWRE (Random Walk in Random Environment) is a classical model for particles moving in a non-homogeneous medium presenting impurities. It consists of a random walk on a graph with random transition probabilities determined by an underlying (static) field of random variables. The long term behavior of RWRE is well-understood, at least on the one-dimensional integer lattice, where trapping effects due to the spatial non-homogeneities lead to very different results than for a standard homogeneous random walk (e.g. non-local recurrence criterion, transient sub-ballistic regimes, anomalous diffusions, sub-exponential large deviations, aging).

In this talk we are interested in perturbing the underlying static random environment by repeatedly re-sampling it from a given law along a sequence of prescribed times, the so-called cooling sequence. This perturbation makes the environment dynamic and the resulting model, recently introduced in the literature, is referred to as RWCRE (Random Walk in Cooling Random Environment).

Depending on the choice of the cooling sequence, RWCRE may present strong homogenization as for a homogeneous Random Walk, or can lead to strong trapping effects as for RWRE. A surprisingly rich palette of possible limit scenarios have been explored in a series of recent papers and ongoing works on the one-dimensional lattice. I plan to give an account of these results and related techniques. Particular emphasis will be given to fluctuations and scaling limits where crossovers and mixtures of different laws emerge as a function of the structure of the cooling sequence.

Based on joint works with Yuki Chino (Taiwan), Conrado da Costa (Durham), Frank den Hollander (Leiden) and Jonathan Peterson (Purdue).