Random walks, Trees, Random environments
Date(s) : 06/11/2024 iCal
10h30 - 12h00
This talk aims to introduce random walks in random environment (RWRE), where the transition probability at each site is random. The long-time behavior of the walk really changes when surrounded by random media, and we would go through the discussion of transience and recurrence, the growth rate of the walk and so on. We focus mainly on one dimension as the theory is quite complete in this case, and situation in higher dimension is more sophisticated. In parallel, we start with the discussion of a similar model known as random walks on trees, and survey hard problems unsolved. If time permits, we would talk about RWRE on trees, and even more specifically, a special (and good) model called random walks in Dirichlet environment (RWDE). It is a well-studied model on high dimensional lattice, and we are able to understand the transient regime of the RWDE on trees, based on a joint work with Dongjian Qian.
This talk requires only basic knowledge of probability like law of large numbers, central limit theorem and conditional expectation. The knowledge of random walks would help but is not necessary. For detailed introduction of RWRE, see “https://arxiv.org/abs/1309.2589”. And for random walks on trees, see “https://rdlyons.pages.iu.edu/prbtree/”.
Our paper could be found at “https://arxiv.org/abs/2405.11845”.
Emplacement
Saint-Charles - FRUMAM (2ème étage)
Catégories
