Fluctuations of the competition interface in presence of shocks Journal Article

Author(s): Ferrari, Patrik L; Nejjar, Peter
Article Title: Fluctuations of the competition interface in presence of shocks
Affiliation IST Austria
Abstract: We consider last passage percolation (LPP) models with exponentially distributed random variables, which are linked to the totally asymmetric simple exclusion process (TASEP). The competition interface for LPP was introduced and studied in Ferrari and Pimentel (2005a) for cases where the corresponding exclusion process had a rarefaction fan. Here we consider situations with a shock and determine the law of the fluctuations of the competition interface around its deter- ministic law of large number position. We also study the multipoint distribution of the LPP around the shock, extending our one-point result of Ferrari and Nejjar (2015).
Keywords: Competition interface; shock; interacting particles; fluctuations
Journal Title: Revista Latino-Americana de Probabilidade e Estatística
Volume: 9
ISSN: 1980-0436
Publisher: ALEA Network  
Date Published: 2017-03-23
Start Page: 299
End Page: 325
Notes: The work of P.L. Ferrari is supported by the German Research Foundation via the SFB 1060–B04 project. P.Nejjar’s work was mostly undertak en while he was a postdoc at Ecole Normale Superieure, Departement de mathematiques et applications, Paris. P. Nejjar was partially supported by ERC Advanced Grant No. 338804.
Open access: yes (repository)