On the 1/n Expansion for Some Unitary Invariant Ensembles of Random Matrices

By Sergio Albeverio, Leonid A. Pastur, Mariya Shcherbina. 2001

101 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/173c97ae7334c81fd7999737cf2bb1770ea228d2

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In Discrete Mathematics and Combinatorics

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Citations in the corpus

Universality of local spectral statistics of random matrices (2011, methodology): “As observed in [2, 61], for analytic V , this term vanishes when we perform a contour integration.”
Asymptotics of unitary and orthogonal matrix integrals (2006, background): “Such ‘topological’ expansions were shown also to hold in the large N limit, and then to match with the formal expansion on a mathematical level of rigor by two authors [16, 17, 23] and previously in the one matrix case in [1, 2] and [12].”
Edge Universality of Beta Ensembles (2013, unknown): “i∈I sup s∈[0,1] K |sαi + (1− s)xi − yK+1| |xi − αi| ) 6 N.”
Asymptotics of the partition function for random matrices via Riemann-Hilbert techniques and applications to graphical enumeration (2002, methodology): “enerating function for counting 2k-valent one-vertex maps (see also (2.24)-(2.26)). There is no inconsistency in this since by duality these two countings are equivalent. Remark 1.5. Additionally, in [2], Albeverio et al have recently considered asymptotic expansions of the form (1.35), for the spec”
Asymptotic Expansion of β Matrix Models in the One-cut Regime (2011, methodology): “.1-5has only one term, namely k= 2g 2 + n, which is present only when k= nmod 2, and likewise for Eqn.1-6which can be considered as the case n= 0. At the asymptotic level, the case = 2 was tackled in [APS01]. For = 1;2;4, the partition function and the correlators can be computed with the help of or”
Universality limits in the bulk for varying measures (2008, unknown): “Then (5.6) ` 1X j=k+1 n (tjn) e Btjn Z t`n tkn e Btd n (t) X̀ j=k n (tjn) e Btjn :”
Second order asymptotics for matrix models (2006, background): “It was shown in [10] (see also [1, 2]) that when m = 1, this enumerative property extends to the free energy of matrix models at all orders, as conjectured and widely used in physics (see, e.”