7 citations · 13 across the 8 of their papers we have counts for
8 papers
Hipster random walks, random series-parallel graph and random homogeneous systems
Xinxing Chen, Thomas Duquesne, Zhan Shi
We study a class of random homogeneous systems. Our main result says that under suitable general assumptions, these systems converge weakly, upon a suitable normalization, to the p…
Infinite differentiability of the free energy for a Derrida-Retaux system
Xinxing Chen
We consider a recursive system which was introduced by Derrida and Retaux (J. Stat. Phys. (2014) 268-290) as a toy model to study the depinning transition in presence o…
The dual Derrida-Retaux conjecture
Xinxing Chen, Yueyun Hu, Zhan Shi
We consider a recursive system which was introduced by Collet et al. [10] as a spin glass model, and later by Derrida, Hakim, and Vannimenus [13] and by Derrida and Retaux…
The sustainability probability for the critical Derrida-Retaux model
Xinxing Chen, Yueyun Hu, Zhan Shi
We are interested in the recursive model studied by Collet, Eckmann, Glaser and Martin [9] and by Derrida and Retaux [12]. We prove that at criticality, the prob…
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…
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…