Point-to-line last passage percolation and the invariant measure of a system of reflecting Brownian motions
| Autor: | Jon Warren, Will FitzGerald |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
60J65 60B20 60K35 Field (physics) Mathematical finance Probability (math.PR) Infimum and supremum Distribution (mathematics) Mathematics::Probability Percolation Line (geometry) FOS: Mathematics Invariant measure Statistical physics Statistics Probability and Uncertainty QA Analysis Brownian motion Mathematics - Probability Mathematics |
| Zdroj: | Fitzgerald, W & Warren, J 2020, ' Point-to-line last passage percolation and the invariant measure of a system of reflecting Brownian motions ', Probability Theory and Related Fields, pp. 121-171 . < https://link.springer.com/article/10.1007/s00440-020-00972-z > |
| ISSN: | 0178-8051 |
| DOI: | 10.1007/s00440-020-00972-z |
| Popis: | This paper proves an equality in law between the invariant measure of a reflected system of Brownian motions and a vector of point-to-line last passage percolation times in a discrete random environment. A consequence describes the distribution of the all-time supremum of Dyson Brownian motion with drift. A finite temperature version relates the point-to-line partition functions of two directed polymers, with an inverse-gamma and a Brownian environment, and generalises Dufresne's identity. Our proof introduces an interacting system of Brownian motions with an invariant measure given by a field of point-to-line log partition functions for the log-gamma polymer. Comment: 41 pages, proofs in Section 4.1 rewritten and minor changes to presentation |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink