arXiv subjects

Temirlan Raimbekov

Publications and source records attributed to Temirlan Raimbekov.

2 recordsLinked to original sources

arXiv2025

Integrable multispecies totally asymmetric stochastic interacting particle systems with homogeneous rates

We study one dimensional stochastic particle systems with exclusion interaction that each site can be occupied by at most one particle, and homogeneous jumping rates. Alimohammadi and Ahmadi previously classified 28 Yang-Baxter integrable two-particle interaction rules for the two species models with homogeneous rates. In this work, we show that 7 of these 28 cases can be naturally extended to integrable models with an arbitrary number of species $N \geq 2$. Moreover, we discover new integrable models with one or two parameters that generalize these 7 cases. For 8 of the remaining 21 cases, we propose an alternative extension scheme that yields integrable $N$ species models.

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arXiv2022

Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles

It has been known that the transition probability of the single species ASEP with $N$ particles is expressed as a sum of $N!$ $N$-fold contour integrals which are related to permutations in the symmetric group $S_N$. On other hand, the transition probabilities of the multi-species ASEP, in general, may be expressed as a sum of much more terms than $N!$. In this paper, we show that if the initial order of species is given by $2\cdots 21$, $12\cdots 2$, $1\cdots 12$ or $21\cdots 1$, then the transition probabilities can be expressed as a sum of at most $N!$ contour integrals, and provide their formulas explicitly.

math-ph↗