Shock fluctuations in asymmetric Hammersley process

• Grant number: 13/20025-8
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: December 01, 2013
• End date: November 30, 2015
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Luiz Renato Gonçalves Fontes
• Grantee: Marcio Watanabe Alves de Souza
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In [16] Ferrari and Fontes proved the variance of the flux across a characteristic is sublinear in a asymmetric simple exclusion process (ASEP). In [22] and [3] Johansson, Baik and Deift gave the first rigorous proofs of the cube root fluctuations of the flux in last passage percolation models (Hammersley process andTasep). Since then a lot of attention have been given to the subject with the intention to extand these fluctuations results to other stationary processes [10], [5], [7], [19], [6]. In the present work will focus on fluctuations results on a system far from equilibrium, more specifically we study an asymmetric version ofHammersley process in the shock regime. The microscopic structure of the shock can be described by a second class particle [14] whose position at time t we denote by Zt. Ferrari and Fontes [15] is the main reference on microscopoic shock fluctuations so far. They proved a central limit theorem and calculate the diffusion coefficient of the shock Zt in the asymmetric exclusion process. The classic Hammersley process(totally asymetric case) were studied by the present author in his Phd thesis were a central limit theorem and diffusion coefficient for Zt were also obtained. Our objective is to extend these results for the asymmetric Hammersley process.