58 citations · 251 across the 36 of their papers we have counts for
5 papers · 1 filter
An infinite-dimensional representation of the Ray-Knight theorems
Elie Aïdékon, Yueyun Hu, Zhan Shi
The classical Ray-Knight theorems for Brownian motion determine the law of its local time process either at the first hitting time of a given value a by the local time at the origi…
The stable Derrida--Retaux system at criticality
Xinxing Chen, Zhan Shi
The Derrida--Retaux recursive system was investigated by Derrida and Retaux (2014) as a hierarchical renormalization model in statistical physics. A prediction of Derrida and Retau…
Results and conjectures on a toy model of depinning
Bernard Derrida, Zhan Shi
We review recent results and conjectures for a simplified version of the depinning problem in presence of disorder which was introduced by Derrida and Retaux in 2014. For this toy…
Path decompositions of perturbed reflecting Brownian motions
Elie Aïdékon, Yueyun Hu, Zhan Shi
We are interested in path decompositions of a perturbed reflecting Brownian motion (PRBM) at the hitting times and at the minimum. Our study relies on the loop soups developed by L…
The critical behaviors and the scaling functions of a coalescence equation
Xinxing Chen, Victor Dagard, Bernard Derrida +1
We show that a coalescence equation exhibits a variety of critical behaviors, depending on the initial condition. This equation was introduced a few years ago to understand a toy m…