Translator Disclaimer
November 2020 Fluctuation lower bounds in planar random growth models
Erik Bates, Sourav Chatterjee
Ann. Inst. H. Poincaré Probab. Statist. 56(4): 2406-2427 (November 2020). DOI: 10.1214/19-AIHP1043

Abstract

We prove $\sqrt{\log n}$ lower bounds on the order of growth fluctuations in three planar growth models (first-passage percolation, last-passage percolation, and directed polymers) under no assumptions on the distribution of vertex or edge weights other than the minimum conditions required for avoiding pathologies. Such bounds were previously known only for certain restrictive classes of distributions. In addition, the first-passage shape fluctuation exponent is shown to be at least $1/8$, extending previous results to more general distributions.

Nous montrons des bornes inférieures de $\sqrt{\log n}$ pour l’ordre des fluctuations de trois modèles planaires de croissance (percolation de premier passage, percolation de dernier passage et polymères dirigés) sans autre hypothèse sur la loi des poids des sommets ou des arêtes que les conditions minimales permettant d’éviter les cas pathologiques. De telles bornes étaient connues auparavant seulement pour certaines classes restreintes de lois. De surcroît, nous montrons que l’exposant des fluctuations autour de la forme limite pour la percolation de premier passage est au moins $1/8$, ce qui étend des résultats précédents à des lois plus générales.

Citation

Download Citation

Erik Bates. Sourav Chatterjee. "Fluctuation lower bounds in planar random growth models." Ann. Inst. H. Poincaré Probab. Statist. 56 (4) 2406 - 2427, November 2020. https://doi.org/10.1214/19-AIHP1043

Information

Received: 4 December 2018; Revised: 10 October 2019; Accepted: 27 November 2019; Published: November 2020
First available in Project Euclid: 21 October 2020

MathSciNet: MR4164842
Digital Object Identifier: 10.1214/19-AIHP1043

Subjects:
Primary: 60E15, 60K35, 60K37, 82D60

Rights: Copyright © 2020 Institut Henri Poincaré

JOURNAL ARTICLE
22 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.56 • No. 4 • November 2020
Back to Top