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math.PR2022
A note on transience of generalized many-dimensional excited random walks
Rodrigo B. Alves, Giulio Iacobelli, Glauco Valle
We consider a variation of the Generalized Excited Random Walk (GERW) in dimension where the lower bound on the drift for excited jumps is time-dependent and decays to zer…
math.CO2022★ 2 cited
A transient equivalence between Aldous-Broder and Wilson's algorithms and a two-stage framework for generating uniform spanning trees
Igor Nunes, Giulio Iacobelli, Daniel Ratton Figueiredo
The and are two well-known algorithms to generate uniform spanning trees (USTs) based on random walks. This work studies their relationship while th…
math.PR2022
Generalized Many-Dimensional Excited Random Walk in Bernoulli Environment
Rodrigo B. Alves, Giulio Iacobelli, Glauco Valle
We study an extension of the generalized excited random walk (GERW) on introduced in [Ann. Probab. 40 (5), 2012, [7]] by Menshikov, Popov, Ramírez and Vachkovskaia.…