Related papers: Asymptotics of the partition function of a random …
We present a method, based on loop equations, to compute recursively, all the terms in the large $N$ topological expansion of the free energy for the 2-hermitian matrix model, in the case where the support of the density of eigenvalues is…
We study products of functions evaluated at self-adjoint polynomials in deterministic matrices and independent Wigner matrices; we compute the deterministic approximations of such products and control the fluctuations. We focus on…
In this short article we propose a full large $N$ asymptotic expansion of the probability that the $m^{\text{th}}$ power of a random unitary matrix of size $N$ has all its eigenvalues in a given arc-interval centered in $1$ when $N$ is…
Asymptotic freeness of independent Haar distributed unitary matrices was discovered by Voiculescu. Many refinements have been obtained, including strong asymptotic freeness of random unitaries and strong asymptotic freeness of random…
We analyze the large degree asymptotic behavior of matrix valued orthogonal polynomials (MVOPs), with a weight that consists of a Jacobi scalar factor and a matrix part. Using the Riemann-Hilbert formulation for MVOPs and the Deift-Zhou…
We present an implementation of the method of orthogonal polynomials which is particularly suitable to study the partition functions of Penner random matrix models, to obtain their explicit forms in the exactly solvable cases, and to…
This work analyzes and compares the asymptotic properties of the covariance matrices of vectors of volume power functionals of random Vietoris-Rips complexes, as the intensity of the underlying homogeneous Poisson point process grows.…
This paper develops a method to carry out the large-$N$ asymptotic analysis of a class of $N$-dimensional integrals arising in the context of the so-called quantum separation of variables method. We push further ideas developed in the…
We solve the loop equations to all orders in $1/N^2$, for the Chain of Matrices matrix model (with possibly an external field coupled to the last matrix of the chain). We show that the topological expansion of the free energy, is, like for…
We study the following question: given a massive Markov random field on $n$ nodes, can a small sample from it provide a rough approximation to the free energy $\mathcal{F}_n = \log{Z_n}$? Results in graph limit literature by Borgs, Chayes,…
In a recent work we have proposed an original analytic expression for the partition function of the quartic oscillator. This partition function, which has a simple and compact form with {\it no adjustable parameters}, reproduces some key…
In this paper, we are interested in matrix valued orthogonal polynomials on the real line with respect to exponential weights. We obtain strong asymptotics as the degree tends to infinity in different regions of the complex plane, as well…
We compute the complete topological expansion of the formal hermitian two-matrix model. For this, we refine the previously formulated diagrammatic rules for computing the 1/ N expansion of the nonmixed correlation functions and give a new…
This dissertation develops, for several families of statistical mechanical and random growth models, techniques for analyzing infinite-volume asymptotics. In the statistical mechanical setting, we focus on the low-temperature phases of spin…
This is a review of the Riemann-Hilbert approach to the large $N$ asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach to…
Voiculescu's freeness emerges in computing the asymptotic of spectra of polynomials on $N\times N$ random matrices with eigenspaces in generic positions: they are randomly rotated with a uniform unitary random matrix $U_N$. In this article…
We study asymptotics of the dimer model on large toric graphs. Let $\mathbb L$ be a weighted $\mathbb{Z}^2$-periodic planar graph, and let $\mathbb{Z}^2 E$ be a large-index sublattice of $\mathbb{Z}^2$. For $\mathbb L$ bipartite we show…
We investigate the analogy between the large N expansion in normal matrix models and the asymptotic expansion of the determinant of the Hilb map, appearing in the study of critical metrics on complex manifolds via projective embeddings.…
We establish the asymptotic expansion in $\beta$ matrix models with a confining, off-critical potential, in the regime where the support of the equilibrium measure is a union of segments. We first address the case where the filling…
In this work we illustrate the resurgent structure of the $\lambda$-deformation; a two-dimensional integrable quantum field theory that has an RG flow with an $SU(N)_k$ Wess-Zumino-Witten conformal fixed point in the UV. To do so we use…