Titulo: Interacting Edge-Reinforced Random Walks
Palestrante: Guilherme Reis  (Technical University of Munich)
Data: 04/09/2023
Horário: 3:30 p.m. to 4:30 p.m.
Sala: C116 - Bloco C - CT – Instituto de Matemática – UFRJ. There will be no transmission online. 

Resumo: Recall that in the simple Random Walk (RW) on Z the walker, starting at 0, just jumps either to the right or to the left with the same probability. It is a classical result that the simple RW on Z is recurrent. In the Edge-Reinforced Random Walk (ERRW) the walker keeps track of the edges already visited and gives extra bias to the edges mostly visited. We would expect that the behavior of the ERRW depends on the strength of the extra bias we decide to give to the edges. The ERRW is a non-markovian process introduced by Diaconis and the first results about it goes back to Davis in 1990. Davis showed, under some assumptions, that the ERRW on Z is either recurrent or it localizes in a single edge with probability 1. What would happen if instead of a single ERRW we consider two or more walkers reinforcing the edges of Z? In an ongoing project, together with Nina Gantert (TUM) and Fabian Michel (TUM), we plan to answer the above question.

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Sincerely,
Organizers: Giulio Iacobelli e Maria Eulalia Vares