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 Parabolic Anderson Model on a Galton-Watson Tree

In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius: The Parabolic Anderson Model on a... [We study the long-time asymptotics of the total mass of the solution to the parabolic Anderson model (PAM) on a supercritical Galton-Watson random tree with bounded degrees. We identify the second-order contribution to this asymptotics in terms of a variational formula that gives information about the local structure of the region where the solution is concentrated. The analysis behind this formula suggests that, under mild conditions on the model parameters, concentration takes place on a tree with minimal degree. Our approach can be applied to locally tree-like finite random graphs, in a coupled limit where both time and graph size tend to infinity. As an example, we consider the configuration model, i.e., uniform simple random graphs with a prescribed degree sequence.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

In and Out of Equilibrium 3: Celebrating Vladas SidoraviciusThe Parabolic Anderson Model on a Galton-Watson Tree

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-kWgrclb8ek

References (19)

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
591 –635
DOI
10.1007/978-3-030-60754-8_25
Publisher site
See Chapter on Publisher Site

Abstract

[We study the long-time asymptotics of the total mass of the solution to the parabolic Anderson model (PAM) on a supercritical Galton-Watson random tree with bounded degrees. We identify the second-order contribution to this asymptotics in terms of a variational formula that gives information about the local structure of the region where the solution is concentrated. The analysis behind this formula suggests that, under mild conditions on the model parameters, concentration takes place on a tree with minimal degree. Our approach can be applied to locally tree-like finite random graphs, in a coupled limit where both time and graph size tend to infinity. As an example, we consider the configuration model, i.e., uniform simple random graphs with a prescribed degree sequence.]

Published: Nov 4, 2020

Keywords: Galton-Watson tree; Sparse random graph; Parabolic Anderson model; Double-exponential distribution; Quenched Lyapunov exponent; 60H25; 82B44; 05C80

There are no references for this article.