Random matrices, non-colliding processes and queues

By Neil O'Connell. 2002

61 citations recorded by the source corpus.

1 Introduction 2 Random matrices and non-colliding Brownian motions 3 A generalisation of Theorem 1 4 An extension of Burke’s theorem 5 Representations for non-colliding processes 6 Output theorems generally 7 First-order asymptotics for directed percolation and directed polymers References

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/15a4da4b2a206a0d135427f7f8a41863049a8e9b

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Citations in the corpus

Nonequilibrium Markov Processes Conditioned on Large Deviations (2014, background): “Applications of these transforms have appeared since Doob’s work in the context of various conditionings of Brownian motion, including the Gaussian and Schrödinger bridges mentioned in the introduction, in addition to non-colliding random walks related to Dyson’s Brownian motion and random matrices ”
A GUE central limit theorem and universality of directed first andlast passage site percolation (2004, background): “By studying a special random variable, Baryshnikov [2] and Gravner, Tracy and Widom [8] (see also [14, 13]) showed that (17) P(D̂k(1) ≤ s) = 1 Zk ∫ s −∞ .”
A path-transformation for random walks and the Robinson-Schensted correspondence (2002, methodology): “ which were recently discovered by Baik, Deift and Johansson [4], Baryshnikov [5] and Gravner, Tracy and Widom [21], between oriented percolation and random matrices. For more background on this, see [33]. The proof of Theorem 1.1 given in [36] uses certain symmetry and reversibility properties of M”
Combinatorial Stochastic Processes (2006, background): “See also [331, 262] and the survey paper [330].”
Tropical Combinatorics and Whittaker functions (2011, unknown): “This theorem has vast generalizations [6, 10, 11, 15, 25, 37, 41, 44, 45, 46, 47, 51], many of which have been obtained via various analogues the ‘Burke property’ discussed in Remark 3.”