Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

In and Out of Equilibrium 3: Celebrating Vladas SidoraviciusThe Stable Derrida–Retaux System at Criticality

In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius: The Stable Derrida–Retaux System at... [The Derrida–Retaux recursive system was investigated by Derrida and Retaux (J Stat Phys 156:268–290, 2014) as a hierarchical renormalization model in statistical physics. A prediction of Derrida and Retaux (J Stat Phys 156:268–290, 2014) on the free energy has recently been rigorously proved (Chen et al., The Derrida–Retaux conjecture on recursive models. https://arxiv.org/abs/1907.01601), confirming the Berezinskii–Kosterlitz–Thouless-type phase transition in the system. Interestingly, it has been established in the paper by Chen et al. that the prediction is valid only under a certain integrability assumption on the initial distribution, and a new type of universality result has been shown when this integrability assumption is not satisfied. We present a unified approach for systems satisfying a certain domination condition, and give an upper bound for derivatives of all orders of the moment generating function. When the integrability assumption is not satisfied, our result allows to identify the large-time order of magnitude of the product of the moment generating functions at criticality, confirming and completing a previous result in Collet et al. (Commun Math Phys 94:353–370, 1984).] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

In and Out of Equilibrium 3: Celebrating Vladas SidoraviciusThe Stable Derrida–Retaux System at Criticality

Part of the Progress in Probability Book Series (volume 77)
Editors: Vares, Maria Eulália; Fernández, Roberto; Fontes, Luiz Renato; Newman, Charles M.

Loading next page...
 
/lp/springer-journals/in-and-out-of-equilibrium-3-celebrating-vladas-sidoravicius-the-stable-pfSNXBvvY1

References (16)

Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
ISBN
978-3-030-60753-1
Pages
239 –264
DOI
10.1007/978-3-030-60754-8_12
Publisher site
See Chapter on Publisher Site

Abstract

[The Derrida–Retaux recursive system was investigated by Derrida and Retaux (J Stat Phys 156:268–290, 2014) as a hierarchical renormalization model in statistical physics. A prediction of Derrida and Retaux (J Stat Phys 156:268–290, 2014) on the free energy has recently been rigorously proved (Chen et al., The Derrida–Retaux conjecture on recursive models. https://arxiv.org/abs/1907.01601), confirming the Berezinskii–Kosterlitz–Thouless-type phase transition in the system. Interestingly, it has been established in the paper by Chen et al. that the prediction is valid only under a certain integrability assumption on the initial distribution, and a new type of universality result has been shown when this integrability assumption is not satisfied. We present a unified approach for systems satisfying a certain domination condition, and give an upper bound for derivatives of all orders of the moment generating function. When the integrability assumption is not satisfied, our result allows to identify the large-time order of magnitude of the product of the moment generating functions at criticality, confirming and completing a previous result in Collet et al. (Commun Math Phys 94:353–370, 1984).]

Published: Nov 4, 2020

Keywords: Derrida-Retaux recursive system; Moment generating function; 60J80; 82B27

There are no references for this article.