Brownian analogues of Burke's theorem

By Neil O'Connell, Marc Yor. 2001

248 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/bde332d2e6398ae1f5de0f20866406ebe714b428

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Citations in the corpus

A Representation for Non-Colliding Random Walks (2002, background): “For x ∈ Rn , let Px denote the law of B started at x, and, for x ∈ W , let P̂x denote the law of the h-transform of B started at x, where h is given by (2).”
Directed polymers and the quantum Toda lattice (2009, methodology): “This is the partition function for a model of a 1 + 1 dimensional directed polymer in a random environment which has been introduced and studied in the papers [38, 42, 54].”
Patterns in eigenvalues: the 70th Josiah Willard Gibbs lecture (2003, methodology): “A wonderful connection between classical queuing theory, tableaux combinatorics and random matrix theory has been developed by Bougerol-Jeulin [18] and by O’Connell-Yor [74].”
ONE-DIMENSIONAL BROWNIAN PARTICLE SYSTEMS WITH RANK DEPENDENT DRIFTS (2007, background): “The Annals of Applied Probability 2008, Vol. 18, No. 6, 2179–2207 DOI: 10.1214/08-AAP516 © Institute of Mathematical Statistics, 2008”
Free Energy Fluctuations for Directed Polymers in Random Media in 1 + 1 Dimension (2012, background): “Theorems 1.3 and 1.10 are proved via asymptotic analysis of a Fredholm determinant formula for the Laplace transform of the O’Connell-Yor semi-discrete directed polymer partition function which we now give as Theorem 1.17.”
Height Fluctuations for the Stationary KPZ Equation (2014, methodology): “ 1.1 and more generally, Theorem 2.13), we start by studying a semi-discrete directed random polymer model with log-gamma boundary sources. This is a mixture of models introduced by O’Connell and Yor [67] and Seppal¨ainen [76]. Indeed, taking M= 0 and τ >0 recovers the semi-discrete directed rand”
Random matrices, non-colliding processes and queues (2002, unknown): “See also [27, 46] for applications in a Brownian context.”
PATTERNS IN EIGENVALUES: THE 70TH JOSIAH WILLARD GIBBS LECTURE (2003, methodology): “A wonderful connection between classical queuing theory, tableaux combinatorics and random matrix theory has been developed by Bougerol-Jeulin [18] and by O’Connell-Yor [74].”
A path-transformation for random walks and the Robinson-Schensted correspondence (2002, methodology): “) t L (µ) = L(µ)P(µ) t . (50) The intertwining relationship (50) can also be veriﬁed directly using QtL = LPt and (46). For related work on reﬂecting Brownian motions and non-colliding diffusions see [7, 11, 12, 13, 16, 23, 35, 39] and references therein. 28 9 Anapplication in queueing theory In thi”
Tropical Combinatorics and Whittaker functions (2011, methodology): “This is the directed polymer model studied in [39], [44], [47], [56].”
From duality to determinants for q-TASEP and ASEP (2012, methodology): “This path integral is essentially the O’Connell-Yor semi-discrete directed polymer partition function [30].”
Limiting shape for directed percolation models (2003, background): “ percolation model— obtained, loosely speaking, by reversing the order of the limits n→ ∞ (in the deﬁnition of g) and α→0—which has been widely studied recently in various contexts; see, for example, [3, 11, 12, 23]. See also [22] for a survey of the connections between these various directed percol”