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Moscow Mathematical Journal, 2020, Volume 20, Number 4, Pages 695–709
DOI: https://doi.org/10.17323/1609-4514-2020-20-4-695-709 (Mi mmj780) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Results and conjectures on a toy model of depinning

Bernard Derridaa, Zhan Shib

a Collège de France, Université PSL, 11 place Marcelin Berthelot, F-75231 Paris Cedex 05, France
b Laboratoire de Probabilités, Statistique et Modélisation (LPSM), Sorbonne Université, 4 place Jussieu, F-75252 Paris Cedex 05, France
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DOI: https://doi.org/10.17323/1609-4514-2020-20-4-695-709
Abstract: 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.
Key words and phrases: hierarchical lattices, depinning transition, Berezinskii–Kosterlitz–Thouless transition.
Document Type: Article
MSC: 60J80, 82B27
Language: English
Citation: Bernard Derrida, Zhan Shi, “Results and conjectures on a toy model of depinning”, Mosc. Math. J., 20:4 (2020), 695–709
Citation in format AMSBIB
\Bibitem{DerShi20}
\by Bernard~Derrida, Zhan~Shi
\paper Results and conjectures on a toy model of~depinning
\jour Mosc. Math.~J.
\yr 2020
\vol 20
\issue 4
\pages 695--709
\mathnet{http://mi.mathnet.ru/mmj780}
\crossref{https://doi.org/10.17323/1609-4514-2020-20-4-695-709}
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