Distributions of a particle’s position and their asymptotics in the q-deformed totally asymmetric zero range process with site dependent jumping rates
| Autor: | Eunghyun Lee, Dong Wang |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Particle system Applied Mathematics 010102 general mathematics Mathematical analysis Asymptotic distribution Fredholm determinant Probability density function Asymmetric simple exclusion process 01 natural sciences 010104 statistics & probability Modeling and Simulation Range (statistics) Probability distribution Initial value problem 0101 mathematics Mathematics |
| Zdroj: | Stochastic Processes and their Applications. 129:1795-1828 |
| ISSN: | 0304-4149 |
| Popis: | In this paper we study the probability distribution of the position of a tagged particle in the q -deformed Totally Asymmetric Zero Range Process ( q -TAZRP) with site dependent jumping rates. For a finite particle system, it is derived from the transition probability previously obtained by Wang and Waugh. We also provide the probability distribution formula for a tagged particle in the q -TAZRP with the so-called step initial condition in which infinitely many particles occupy one single site and all other sites are unoccupied. For the q -TAZRP with step initial condition, we provide a Fredholm determinant representation for the probability distribution function of the position of a tagged particle, and moreover we obtain the limiting distribution function as the time goes to infinity. Our asymptotic result for q -TAZRP with step initial condition is comparable to the limiting distribution function obtained by Tracy and Widom for the k th leftmost particle in the asymmetric simple exclusion process with step initial condition (Theorem 2 in Tracy and Widom (2009)). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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