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pro vyhledávání: '"Sabot, Christophe"'
In this paper we study the recurrence and transience of the $\mathbb{Z}^d$-valued branching random walk in random environment indexed by a critical Bienaym\'e-Galton-Watson tree, conditioned to survive. The environment is made either of random conduc
Externí odkaz:
http://arxiv.org/abs/2406.17622
Autor:
Sabot, Christophe, Tarrès, Pierre
In this paper we continue the analysis, initiated in the paper *-VRJP I, of the *-Vertex Reinforced Jump Process (*-VRJP), which is a non reversible generalization of the Vertex Reinforced Jump Process (VRJP). More precisely, we give a representation
Externí odkaz:
http://arxiv.org/abs/2401.02782
This paper presents a multidimensional extension of the Matsumoto-Yor properties related to exponential functionals of drifted Brownian motion. The extension involves the interaction of geometric Brownian motions which are indexed by the vertices of
Externí odkaz:
http://arxiv.org/abs/2306.02158
Publikováno v:
In Stochastic Processes and their Applications September 2024 175
Autor:
Sabot, Christophe, Tarrès, Pierre
We introduce a non-reversible generalization of the Vertex-Reinforced Jump Process (VRJP), which we call *-Vertex-Reinforced Jump Process (*-VRJP). It can be seen as the continuous-time counterpart of the *-Edge-Reinforced Random Walk (*-ERRW) (see B
Externí odkaz:
http://arxiv.org/abs/2102.08988
We define a generalisation of the Edge-Reinforced Random Walk (ERRW) introduced by Coppersmith and Diaconis in 1986, called *-Edge-Reinforced Random Walk (*-ERRW), which can be seen as an extension of the r-dependent ERRW introduced by Bacallado (201
Externí odkaz:
http://arxiv.org/abs/2102.08984
A classic result on the 1-dimensional Brownian motion shows that conditionally on its first hitting time of 0, it has the distribution of a 3-dimensional Bessel bridge. By applying a certain time-change to this result, Matsumoto and Yor showed a theo
Externí odkaz:
http://arxiv.org/abs/2004.10692
Publikováno v:
Electronic Journal of Probability 26, 1-25, 2021
Using a divergent Bass-Burdzy flow we construct a self-repelling one-dimensional diffusion. Heuristically, it can be interpreted as a solution to an SDE with a singular drift involving a derivative of the local time. We show that this self-repelling
Externí odkaz:
http://arxiv.org/abs/1910.06836
Autor:
Sabot, Christophe
We prove polynomial decay of the mixing field of the Vertex Reinforced Jump Process (VRJP) on $\Bbb{Z}^2$ with bounded conductances. Using [17] we deduce that the VRJP on $\Bbb{Z}^2$ with any constant conductances is almost surely recurrent. It gives
Externí odkaz:
http://arxiv.org/abs/1907.07949
Autor:
Orenshtein, Tal, Sabot, Christophe
Publikováno v:
Electronic Journal of Probability 25 (2020) paper 33
We consider one-dependent random walks on $\mathbb{Z}^d$ in random hypergeometric environment for $d\ge 3$. These are memory-one walks in a large class of environments parameterized by positive weights on directed edges and on pairs of directed edges
Externí odkaz:
http://arxiv.org/abs/1804.01406