Random Matrices and Random Permutations

By P. Moerbeke. 2000

197 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Computer Vision and Pattern Recognition, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/fa248c8badd82910cb6698bc9fbe5b030f988a72

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Citations in the corpus

The Surprising Mathematics of Longest Increasing Subsequences (2015, result): “This conjecture was given three different proofs soon afterwards, one by Andrei Okounkov [95],3 and two other roughly equivalent ones found independently by Alexei Borodin, Grigori Olshanski, and Andrei Okounkov [19] and by Kurt Johansson [63].”
PATTERNS IN EIGENVALUES: THE 70TH JOSIAH WILLARD GIBBS LECTURE (2003, methodology): “For work of Okounkov, connecting random matrices and random permutations through Riemann surfaces, see [75].”
Gromov-Witten theory, Hurwitz numbers, and Matrix models, I (2001, methodology): “er studying the asymptotic enumeration of branching graphs on Σg with lcells, we see that the problem is exactly parallel to the asymptotic enumeration of simple maps on Σg with lcells carried out in [68]. As in the case of branching graphs, there exist only ﬁnitely many homotopy types of simple map”
Stein’s method and Plancherel measure of the symmetric group (2003, methodology): “stical properties of partitions chosen from Plancherel measure. As it is beyond the scope of this paper to survey the topic, we refer the reader to the surveys [AlD], [De] and the seminal papers [J], [O], [BOO] for a glimpse of the remarkable recent work on Plancherel measure. A purpose of the prese”
Kerov’s Central Limit Theorem for the Plancherel Measure on Young Diagrams (2003, background): “e limit distribution of the same number of (properly scaled) largest eigenvalues of the random Hermitian N ×N matrix taken from the Gaussian Unitary Ensemble, as N →∞. See [BDJ] and subsequent papers [Ok], [BOO], [Jo3], [Jo4], [BDR]. It turns out that the striking similarity between these two random”
Eigenvalue statistics for beta-ensembles (2003, background): “We obtain a duality principle (between β and 2/β) for the (normalized) Jack polynomial average over the corresponding β-Hermite ensemble; we also obtain a simple proof for a conjecture of Goulden and Jackson [36], first proved by Okounkov [73].”
Heisenberg algebra and a graphical calculus (2010, methodology): “Products of these moments were investigated in [20, 33, 38, 40] in relation to the asymptotic representation theory of the symmetric group and free probability.”
Generating random density matrices (2010, unknown): “[46, 47].”
Infinite wedge and random partitions (1999, methodology): “unctions was used in [7] and [17], independently, to give an analytic proof of a conjecture due to Baik, Deift, and Johansson [1, 2] (a combinatorial proof of that conjecture was suggested earlier in [25]). For similar questions related to the more general z-measures see [10, 17, 28]. In [7], the as”
Distribution Functions for Largest Eigenvalues and Their Applications (2002, methodology): “The full conjecture was proved by Okounkov [33] using topological methods and by Johansson [23] and by Borodin, Okounkov and Olshanski [10] using analytical methods.”
Universality for mathematical and physical systems (2006, unknown): “ of a GUE matrix. This conjecture was proved for the 2nd row in [BDJ2]. For general k, the conjecture was proved, with convergence in joint distribution, in three separate papers in rapid succession ([Oko], [BOO], [Joh1]), using very diﬀerent methods. The proof in [Oko] relies on an interplay betwee”
The Brownian map is the scaling limit of uniform random plane quadrangulations (2011, unknown): “See [27], [6], [26] and [2] for instance.”
Gaussian fluctuations of characters of symmetric groups and of Young diagrams (2005, background): “ exact formulas. Such formulas for the moments of large classes of random matrices were known for a long time and they can be viewed as series indexed by two-dimensional surfaces [Zvo97] and Okounkov [Oko00] found their counterpart for random Young diagrams distributed according to the Plancherel me”