Large deviations for disordered bosons and multiple orthogonal polynomial ensembles
TLDR
In this paper, a large deviations principle for the empirical measures of a class of biorthogonal and multiple orthogonal polynomial ensembles was proved for disordered bosons.Abstract:
We prove a large deviations principle for the empirical measures of a class of biorthogonal and multiple orthogonal polynomial ensembles that includes biorthogonal Laguerre, Jacobi, and Hermite ensembles, the matrix model of Lueck, Sommers, and Zirnbauer for disordered bosons, the Stieltjes-Wigert matrix model of Chern-Simons theory, and Angelesco ensembles.read more
Citations
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Full length article: Weakly admissible vector equilibrium problems
TL;DR: This work establishes lower semi-continuity and strict convexity of the energy functionals for a large class of vector equilibrium problems in logarithmic potential theory and implies the existence and uniqueness of a minimizer for suchvector equilibrium problems.
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Biorthogonal ensembles with two-particle interactions
Tom Claeys,Stefano Romano +1 more
TL;DR: In this article, the authors investigated determinantal point processes on [0, + ∞) of the form and proved that the biorthogonal polynomials associated with such models satisfy a recurrence relation and a Christoffel-Darboux formula.
A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2005{2009
TL;DR: (2 < p < 4) [200].
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A large deviation principle for Wigner matrices without Gaussian tails
Charles Bordenave,Pietro Caputo +1 more
TL;DR: In this paper, a large deviation principle was established for the empirical spectral measure of Hermitian matrices with iid entries, whose tail probabilities behave like $e^{-at^{\alpha}}$ for some $a>0$ and $\alpha \in(0,2)$.
Journal ArticleDOI
The local universality of Muttalib-Borodin biorthogonal ensembles with parameter $\theta = \frac{1}{2}$
A. B. J. Kuijlaars,L. D. Molag +1 more
TL;DR: In this article, the Deift-Zhou steepest descent method was used to obtain the matching condition of the local parametrix at the origin of the Biorthogonal Ensemble.
References
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Book
Large Deviations Techniques and Applications
Amir Dembo,Ofer Zeitouni +1 more
TL;DR: The LDP for Abstract Empirical Measures and applications-The Finite Dimensional Case and Applications of Empirically Measures LDP are presented.
Book
Probability measures on metric spaces
TL;DR: The Borel subsets of a metric space Probability measures in the metric space and probability measures in a metric group Probability measure in locally compact abelian groups The Kolmogorov consistency theorem and conditional probability probabilistic probability measures on $C[0, 1]$ and $D[0-1]$ Bibliographical notes Bibliography List of symbols Author index Subject index as mentioned in this paper
BookDOI
Entropy, large deviations, and statistical mechanics
TL;DR: In this paper, the authors introduce the concept of large deviations for random variables with a finite state space, which is a generalization of the notion of large deviation for random vectors.
Book
An Introduction to Random Matrices
TL;DR: The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic and combinatorial) as mentioned in this paper.