{"title":"$q$-TASEP的tracy - wisdom渐近性","authors":"P. Ferrari, B. Vető","doi":"10.1214/14-AIHP614","DOIUrl":null,"url":null,"abstract":"We consider the q-TASEP that is a q-deformation of the totally asymmetric simple exclusion process (TASEP) on Z for q in [0,1) where the jump rates depend on the gap to the next particle. For step initial condition, we prove that the current fluctuation of q-TASEP at time t are of order t^{1/3} and asymptotically distributed as the GUE Tracy-Widom distribution, which confirms the KPZ scaling theory conjecture.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"32 1","pages":"1465-1485"},"PeriodicalIF":1.2000,"publicationDate":"2013-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"60","resultStr":"{\"title\":\"Tracy–Widom asymptotics for $q$-TASEP\",\"authors\":\"P. Ferrari, B. Vető\",\"doi\":\"10.1214/14-AIHP614\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the q-TASEP that is a q-deformation of the totally asymmetric simple exclusion process (TASEP) on Z for q in [0,1) where the jump rates depend on the gap to the next particle. For step initial condition, we prove that the current fluctuation of q-TASEP at time t are of order t^{1/3} and asymptotically distributed as the GUE Tracy-Widom distribution, which confirms the KPZ scaling theory conjecture.\",\"PeriodicalId\":7902,\"journal\":{\"name\":\"Annales De L Institut Henri Poincare-probabilites Et Statistiques\",\"volume\":\"32 1\",\"pages\":\"1465-1485\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2013-10-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"60\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales De L Institut Henri Poincare-probabilites Et Statistiques\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1214/14-AIHP614\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/14-AIHP614","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
We consider the q-TASEP that is a q-deformation of the totally asymmetric simple exclusion process (TASEP) on Z for q in [0,1) where the jump rates depend on the gap to the next particle. For step initial condition, we prove that the current fluctuation of q-TASEP at time t are of order t^{1/3} and asymptotically distributed as the GUE Tracy-Widom distribution, which confirms the KPZ scaling theory conjecture.
期刊介绍：
The Probability and Statistics section of the Annales de l’Institut Henri Poincaré is an international journal which publishes high quality research papers. The journal deals with all aspects of modern probability theory and mathematical statistics, as well as with their applications.
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