{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,19]],"date-time":"2025-03-19T11:17:45Z","timestamp":1742383065278},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:p>The main aim of this paper is to prove the quenched central limit theorem for reversible random walks in a stationary random environment on <jats:bold>Z<\/jats:bold> without having the integrability condition on the conductance and without using any martingale. The method shown here is particularly simple and was introduced by Depauw and Derrien [3]. More precisely, for a given realization \u03c9 of the environment, we consider the Poisson equation (<jats:italic>P<\/jats:italic>\n               <jats:sub>\u03c9<\/jats:sub> - <jats:italic>I<\/jats:italic>)<jats:italic>g<\/jats:italic> = <jats:italic>f<\/jats:italic>, and then use the pointwise ergodic theorem in [8] to treat the limit of solutions and then the central limit theorem will be established by the convergence of moments. In particular, there is an analogue to a Markov process with discrete space and the diffusion in a stationary random environment.<\/jats:p>","DOI":"10.1017\/s0021900200011979","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T14:51:14Z","timestamp":1459263074000},"page":"1051-1064","source":"Crossref","is-referenced-by-count":1,"title":["A Quenched Central Limit Theorem for Reversible Random Walks in a Random Environment on Z"],"prefix":"10.1017","volume":"51","author":[{"given":"Hoang-Chuong","family":"Lam","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,2,4]]},"reference":[{"key":"S0021900200011979_ref5","first-page":"61","volume":"40","year":"1985","journal-title":"Uspekhi Mat. Nauk"},{"key":"S0021900200011979_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01010495"},{"key":"S0021900200011979_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2009.01.030"},{"key":"S0021900200011979_ref2","volume-title":"Probability and Measure","year":"1995"},{"key":"S0021900200011979_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-007-9465-z"},{"key":"S0021900200011979_ref9","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/39\/40\/R01"},{"key":"S0021900200011979_ref8","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-39-00501-6"},{"key":"S0021900200011979_ref7","first-page":"547","volume-title":"Statistics and Probability: Essays in Honor of C. R. Rao","year":"1982"},{"key":"S0021900200011979_ref1","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1032374457"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200011979","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T09:17:52Z","timestamp":1682500672000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200011979\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12]]},"references-count":9,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2014,12]]}},"alternative-id":["S0021900200011979"],"URL":"https:\/\/doi.org\/10.1017\/s0021900200011979","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12]]}}}