Second Class Particle Behaviour in Blocking ASEP
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910143946424320 |
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| author | Adams, Daniel Balázs, Márton Jay, Jessica |
| author_facet | Adams, Daniel Balázs, Márton Jay, Jessica |
| contents | We consider any fixed $d\in\mathbb{Z}_{>0}$ number of second class particles in the asymmetric simple exclusion process (ASEP), constructed via a basic coupling of two ASEPs. We give the joint distribution of the positions of the second class particles and also the probability of there being a second class particle at a given site, under the natural blocking measure for ASEP. In order to find these distributions we use results about the number of particles in half-infinite and finite site ranges of ASEP. Our investigations also lead to probabilistic proofs of well-known combinatorial identities; the Durfee rectangles identity, Euler's identity, and the $q$-Binomial Theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_16769 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Second Class Particle Behaviour in Blocking ASEP Adams, Daniel Balázs, Márton Jay, Jessica Probability Combinatorics Number Theory 60K35, 11P84, 05A19 We consider any fixed $d\in\mathbb{Z}_{>0}$ number of second class particles in the asymmetric simple exclusion process (ASEP), constructed via a basic coupling of two ASEPs. We give the joint distribution of the positions of the second class particles and also the probability of there being a second class particle at a given site, under the natural blocking measure for ASEP. In order to find these distributions we use results about the number of particles in half-infinite and finite site ranges of ASEP. Our investigations also lead to probabilistic proofs of well-known combinatorial identities; the Durfee rectangles identity, Euler's identity, and the $q$-Binomial Theorem. |
| title | Second Class Particle Behaviour in Blocking ASEP |
| topic | Probability Combinatorics Number Theory 60K35, 11P84, 05A19 |
| url | https://arxiv.org/abs/2305.16769 |