On the chemical distance exponent for the two-sided level set of the two-dimensional Gaussian free field

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2022-01-01 DOI:10.30757/alea.v19-28

Yifan Gao, Fuxi Zhang

引用次数: 0

Abstract

. In this paper we study the two-sided level set of the two-dimensional discrete Gaussian free ﬁeld (GFF), where a site is open if the absolute value of the GFF at this site is at most λ for a ﬁxed parameter λ > 0 . For the GFF on a box of size N with Dirichlet boundary conditions, we show that there exists (cid:15) > 0 such that with probability tending to 1 as N → ∞ , all the open paths whose Euclidean diameters are of order N have lengths larger than N 1+ (cid:15) .

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二维高斯自由场的双边水平集的化学距离指数

。本文研究了二维离散高斯自由场(GFF)的双面水平集，对于一个固定参数λ > 0，当GFF的绝对值不超过λ时，该位置是开放的。对于具有Dirichlet边界条件的大小为N的盒子上的GFF，我们证明了存在(cid:15) > 0，使得当N→∞时，欧几里德直径为N阶的所有开放路径的长度都大于n1 + (cid:15)，且概率趋于1。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Alea-Latin American Journal of Probability and Mathematical Statistics STATISTICS & PROBABILITY-

CiteScore

1.10

自引率

0.00%

发文量

期刊介绍： ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.