{"title":"On the chemical distance exponent for the two-sided level set of the two-dimensional Gaussian free field","authors":"Yifan Gao, Fuxi Zhang","doi":"10.30757/alea.v19-28","DOIUrl":null,"url":null,"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) .","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":"1 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Alea-Latin American Journal of Probability and Mathematical Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.30757/alea.v19-28","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
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) .
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.
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