相关论文: Replica Approach in Random Matrix Theory

In the last few years several new Random Matrix Models have been proposed and studied. They have found application in various different contexts, ranging from the physics of mesoscopic systems to the chiral transition in lattice gauge…

This review article provides an overview of random matrix theory (RMT) with a focus on its growing impact on the formulation and inference of statistical models and methodologies. Emphasizing applications within high-dimensional statistics,…

Matrix functions are a central topic of linear algebra, and problems requiring their numerical approximation appear increasingly often in scientific computing. We review various limited-memory methods for the approximation of the action of…

By exhibiting the corresponding Lax pair representations we propose a wide class of integrable two-dimensional (2D) fermionic Toda lattice (TL) hierarchies which includes the 2D N=(2|2) and N=(0|2) supersymmetric TL hierarchies as…

I discuss the connection between the Hamiltonian and path integral approaches for fermionic fields. I show how the temporal Wilson projection operators appear naturally in a lattice action. I also carefully treat the insertion of a chemical…

First we survey generating function methods for obtaining useful probability estimates about random matrices in the finite classical groups. Then we describe a probabilistic picture of conjugacy classes which is coherent and beautiful.…

We point out a simple criterion for convergence of polynomials to a concrete entire function in the Laguerre-P\'{o}lya ($\mathcal{LP}$) class (of all functions arising as uniform limits of polynomials with only real roots). We then use this…

This chapter is a pedagogical review of the Hubbard model for bosons with repulsion and for fermions with attraction and repulsion primarily using two methods, one chosen for its simplicity and insights (mean field theory) and the other…

We suggest a new mean field method for studying the thermodynamic competition between magnetic and superconducting phases in a two-dimensional square lattice. A partition function is constructed by writing microscopic interactions that…

We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these…

Response functions are a fundamental aspect of physics; they represent the link between experimental observations and the underlying quantum many-body state. However, this link is often under-appreciated, as the Lehmann formalism for…

In a recent contribution [arXiv:0904:4151] entanglement renormalization was generalized to fermionic lattice systems in two spatial dimensions. Entanglement renormalization is a real-space coarse-graining transformation for lattice systems…

We propose an algorithm for low rank matrix completion for matrices with binary entries which obtains explicit binary factors. Our algorithm, which we call TBMC (\emph{Tiling for Binary Matrix Completion}), gives interpretable output in the…

The continuum limit and scaling properties of an asymptotically free field theory regularized on a random lattice are compared with those on a regular square lattice. We work on random lattices parametrized by a degree of ``randomness''…

The average of the ratio of powers of the spectral determinants of the Dirac operator in the $\epsilon$-regime of QCD is shown to satisfy a Toda lattice equation. The quenched limit of this Toda lattice equation is obtained using the…

We apply the cavity method to a spin glass model on a `small world' lattice, a random bond graph super-imposed upon a 1-dimensional ferromagnetic ring. We show the correspondence with a replicated transfer matrix approach, up to the level…

Some elementary rigorous remark about the replica formalism in the Statistical Physics' approach to threshold phenomena in Computational Complexity Theory is presented.

We consider a nonlinear field equation which can be derived from a binomial lattice as a continuous limit. This equation, containing a perturbative friction-like term and a free parameter $\gamma$, reproduces the Toda case (in absence of…

I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees…

Results on the finite nonperiodic Toda lattice are extended to some generalizations of the system: The relativistic Toda lattice, the generalized Toda lattice associated with simple Lie groups and the full Kostant-Toda lattice. The areas…