Moscow Mathematical Journal

Volume 20, Issue 4, October–December 2020 pp. 695–709.

Results and Conjectures on a Toy Model of Depinning

Authors: Bernard Derrida (1) and Zhan Shi (2)
Author institution:(1) Collège de France, Université PSL, 11 place Marcelin Berthelot, F-75231 Paris Cedex 05, France
(2) Laboratoire de Probabilités, Statistique et Modélisation (LPSM), Sorbonne Université, 4 place Jussieu, F-75252 Paris Cedex 05, France

Summary:

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 model, the depinning transition has been predicted to be of the Berezinskii–Kosterlitz–Thouless type. Here we discuss under which conditions this prediction can be proved and how it is modified otherwise.

2010 Math. Subj. Class. 60J80, 82B27.

Keywords: Hierarchical lattices, depinning transition, Berezinskii–Kosterlitz–Thouless transition.

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