7 citations · 13 across the 10 of their papers we have counts for
14 papers
Local limit theorems on relatively hyperbolic groups with respect to virtually nilpotent subgroups
Matthieu Dussaule
Given a probability measure on a finitely generated group, the local limit problem consists in finding asymptotics of , the probability that the random walk at time i…
The growth of the Green function for random walks and Poincar{é} series
Matthieu Dussaule, Wenyuan Yang, Longmin Wang
Given a probability measure on a finitely generated group , the Green function encodes many properties of the random walk associated with . Finding asymptotics…
Exotic local limit theorems at the phase transition in free products
Matthieu Dussaule, Marc Peigné, Samuel Tapie
We construct random walks on free products of the form Z 3 * Z d , with d = 5 or 6 which are divergent and not spectrally positive recurrent. We then derive a local limit theorem f…
Ratio-limit boundaries for random walks on relatively hyperbolic groups
Adam Dor-On, Matthieu Dussaule, Ilya Gekhtman
We study boundaries arising from limits of ratios of transition probabilities for random walks on relatively hyperbolic groups. We extend, as well as determine significant limitati…
Branching Random Walks on relatively hyperbolic groups
Matthieu Dussaule, Longmin Wang, Wenyuan Yang
Let be a non-elementary relatively hyperbolic group with a finite generating set. Consider a finitely supported admissible and symmetric probability measure on and a pr…
A local limit theorem for convergent random walks on relatively hyperbolic groups
Matthieu Dussaule, Marc Peigné, Samuel Tapie
We study random walks on relatively hyperbolic groups whose law is convergent, in the sense that the derivative of its Green function is finite at the spectral radius.When paraboli…
The Hausdorff dimension of the harmonic measure for relatively hyperbolic groups
Matthieu Dussaule, Wenyuan Yang
The paper studies the Hausdorff dimension of harmonic measures on various boundaries of a relatively hyperbolic group which are associated with random walks driven by a probability…
An embedding of the Morse boundary in the Martin boundary
Matthew Cordes, Matthieu Dussaule, Ilya Gekhtman
We construct a one-to-one continuous map from the Morse boundary of a hierarchically hyperbolic group to its Martin boundary. This construction is based on deviation inequalities g…
Local limit theorems in relatively hyperbolic groups II : the non-spectrally degenerate case
Matthieu Dussaule
This is the second of a series of two papers dealing with local limit theorems in relatively hyperbolic groups. In this second paper, we restrict our attention to non-spectrally de…
Local limit theorems in relatively hyperbolic groups I : rough estimates
Matthieu Dussaule
This is the first of a series of two papers dealing with local limit theorems in relatively hyperbolic groups. In this first paper, we prove rough estimates for the Green function.…
Stability phenomena for Martin boundaries of relatively hyperbolic groups
Matthieu Dussaule, Ilya Gekhtman
Let be a relatively hyperbolic group and let be an admissible symmetric finitely supported probability measure on . We extend Floyd-Ancona type inequalities up to the sp…
Entropy and drift for word metric on relatively hyperbolic groups
Matthieu Dussaule, Ilya Gekhtman
We are interested in the Guivarc'h inequality for admissible random walks on finitely generated relatively hyperbolic groups, endowed with a word metric. We show that for random wa…
The Martin boundary of relatively hyperbolic groups with virtually abelian parabolic subgroups
Matthieu Dussaule, Ilya Gekhtman, Victor Gerasimov +1
Given a probability measure on a finitely generated group, its Martin boundary is a way to compactify the group using the Green's function of the corresponding random walk. We give…
The martin boundary of a free product of abelian groups
Matthieu Dussaule
Given a probability measure on a finitely generated group, its Martin boundary is a way to compactify the group using the Green function of the corresponding random walk. It is kno…