Last passage percolation in lower triangular domain
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915404326109184 |
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| author | Betea, Dan Nazarov, Anton Nikitin, Pavel |
| author_facet | Betea, Dan Nazarov, Anton Nikitin, Pavel |
| contents | Last passage percolation (LPP) in an $n\times n$ lower triangular domain has nice connections with various generalizations of Schur measures. LPP along an anti-diagonal, from $(1,n)$ to $(n,1)$, gives a distribution of a highest column of a random composition with respect to a Demazure measure (a non-symmetric analog of a Schur measure). LPP along a main diagonal, from $(1,1)$ to $(n,n)$, is distributed as a marginal of a Pfaffian Schur process. In the first case we show that the asymptotics for the constant specialization is governed by the GOE Tracy-Widom distribution, in the second case - by the GSE Tracy-Widom distribution. In the latter case we were also able to study the truncated lower triangular case, obtaining an interesting generalization of the GSE Tracy-Widom distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16320 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Last passage percolation in lower triangular domain Betea, Dan Nazarov, Anton Nikitin, Pavel Representation Theory Combinatorics Probability 60C05 (Primary) 60G55, 05A19 (Secondary) Last passage percolation (LPP) in an $n\times n$ lower triangular domain has nice connections with various generalizations of Schur measures. LPP along an anti-diagonal, from $(1,n)$ to $(n,1)$, gives a distribution of a highest column of a random composition with respect to a Demazure measure (a non-symmetric analog of a Schur measure). LPP along a main diagonal, from $(1,1)$ to $(n,n)$, is distributed as a marginal of a Pfaffian Schur process. In the first case we show that the asymptotics for the constant specialization is governed by the GOE Tracy-Widom distribution, in the second case - by the GSE Tracy-Widom distribution. In the latter case we were also able to study the truncated lower triangular case, obtaining an interesting generalization of the GSE Tracy-Widom distribution. |
| title | Last passage percolation in lower triangular domain |
| topic | Representation Theory Combinatorics Probability 60C05 (Primary) 60G55, 05A19 (Secondary) |
| url | https://arxiv.org/abs/2507.16320 |