The Derrida--Retaux conjecture on recursive models

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The Derrida--Retaux conjecture on recursive models. / Лифшиц, Михаил Анатольевич; Ши, Зан.

In: Annals of Probability, Vol. 49, No. 2, 25.03.2021, p. 637-670.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{d1e214469fdc443dac4b98ce5fa82786,

title = "The Derrida--Retaux conjecture on recursive models",

abstract = "We are interested in the nearly supercritical regime in a family of maxtype recursive models studied by Collet, Eckman, Glaser and Martin (Comm. Math. Phys. 94 (1984) 353-370) and by Derrida and Retaux (J. Stat. Phys. 156 (2014) 268-290) and prove that, under a suitable integrability assumption on the initial distribution, the free energy vanishes at the transition with an essential singularity with exponent J. This gives a weaker answer to a conjecture of Derrida and Retaux (J. Stat. Phys. 156 (2014) 268-290). Other behaviours are obtained when the integrability condition is not satisfied.",

keywords = "Max-type recursive model, critical behavior, depinning transition. We are going to see that p < 1, free energy, SPIN-GLASS, ITERATED FUNCTIONS, DISORDER, depinning transition",

author = "Лифшиц, {Михаил Анатольевич} and Зан Ши",

year = "2021",

month = mar,

day = "25",

doi = "10.1214/20-AOP1457",

language = "English",

volume = "49",

pages = "637--670",

journal = "Annals of Probability",

issn = "0091-1798",

publisher = "Institute of Mathematical Statistics",

number = "2",

}

RIS

TY - JOUR

T1 - The Derrida--Retaux conjecture on recursive models

AU - Лифшиц, Михаил Анатольевич

AU - Ши, Зан

PY - 2021/3/25

Y1 - 2021/3/25

N2 - We are interested in the nearly supercritical regime in a family of maxtype recursive models studied by Collet, Eckman, Glaser and Martin (Comm. Math. Phys. 94 (1984) 353-370) and by Derrida and Retaux (J. Stat. Phys. 156 (2014) 268-290) and prove that, under a suitable integrability assumption on the initial distribution, the free energy vanishes at the transition with an essential singularity with exponent J. This gives a weaker answer to a conjecture of Derrida and Retaux (J. Stat. Phys. 156 (2014) 268-290). Other behaviours are obtained when the integrability condition is not satisfied.

AB - We are interested in the nearly supercritical regime in a family of maxtype recursive models studied by Collet, Eckman, Glaser and Martin (Comm. Math. Phys. 94 (1984) 353-370) and by Derrida and Retaux (J. Stat. Phys. 156 (2014) 268-290) and prove that, under a suitable integrability assumption on the initial distribution, the free energy vanishes at the transition with an essential singularity with exponent J. This gives a weaker answer to a conjecture of Derrida and Retaux (J. Stat. Phys. 156 (2014) 268-290). Other behaviours are obtained when the integrability condition is not satisfied.

KW - Max-type recursive model

KW - critical behavior

KW - depinning transition. We are going to see that p < 1

KW - free energy

KW - SPIN-GLASS

KW - ITERATED FUNCTIONS

KW - DISORDER

KW - depinning transition

UR - http://www.scopus.com/inward/record.url?scp=85113665051&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/be3218a8-a82e-3966-875e-1dd1331d45e2/

U2 - 10.1214/20-AOP1457

DO - 10.1214/20-AOP1457

M3 - Article

VL - 49

SP - 637

EP - 670

JO - Annals of Probability

JF - Annals of Probability

SN - 0091-1798

IS - 2

ER -

ID: 75370703