相关论文: Replica Approach in Random Matrix Theory

In this paper we introduce a family of rational approximations of the reciprocal of a $\phi$-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The…

Matrix models play an important role in studies of quantum gravity, being candidates for a formulation of M-theory, but are notoriously difficult to solve. In this work, we present a fresh approach by introducing a novel exact model…

A very elementary model of a single positive hermitian random matrix coupled to an external matrix is defined and studied. Expanding the exact effective action around its classical solution leads to the ``quantum Penner action'', from which…

A new technique is proposed to classify a topological field in abelian lattice gauge theories. We perform the classification by regarding the topological field as a local composite field of the gauge field tensor instead of the vector…

Prompt isolated leptons are essential in many analyses in high-energy particle physics but are subject to fake-lepton background, i.e. objects that mimic the lepton signature. The fake-lepton background is difficult to estimate from…

We present one loop boundary reflection matrix for $d_4^{(1)}$ Toda field theory defined on a half line with the Neumann boundary condition. This result demonstrates a nontrivial cancellation of non-meromorphic terms which are present when…

We reexamine the external field problem for $N\times N$ hermitian one-matrix models. We prove an equivalence of the models with the potentials $\tr{({1/over2N}X^2 + \log X - \Lambda X)}$ and $\sum_{k=1}^\infty t_k\tr{X^k}$ providing the…

An effective quantum field theory of the 2D Hubbard model on a square lattice near half-filling is presented and studied. This effective model describes so-called nodal and antinodal fermions, and it is derived from the lattice model using…

We introduce a finite version of free probability for rectangular matrices that amounts to operations on singular values of polynomials. We show that we can replicate the transforms from free probability, and that asymptotically there is…

We consider monotonic, multiple regression for a set of contiguous regions (lattice data). The regression functions permissibly vary between regions and exhibit geographical structure. We develop new Bayesian non-parametric methodology…

The Hartree-Fock-RPA approach is applied to the 1D anti-ferromagnetic Heisenberg model in the Jordan-Wigner representation. Somewhat contrary to expectation, this leads to reasonable results for spectral functions and sum rules in the…

Bi-Hamiltonian structure and Lax pair formulation with the spectral parameter of the generalized fermionic Toda lattice hierarchy as well as its bosonic and fermionic symmetries for different (including periodic) boundary conditions are…

Motivated by the asymptotic collective behavior of random and deterministic matrices, we propose an approximation (called "free deterministic equivalent") to quite general random matrix models, by replacing the matrices with operators…

We derive a new kind of recursion relation to obtain the one-particle-irreducible (1PI) Feynman diagrams for the effective action. By using this method, we have obtained the graphical representation of the four-loop effective action in case…

A sparse random block matrix model suggested by the Hessian matrix used in the study of elastic vibrational modes of amorphous solids is presented and analyzed. By evaluating some moments, benchmarked against numerics, differences in the…

In these lectures we discuss some elementary concepts in connection with the theory of symmetric spaces applied to ensembles of random matrices. We review how the relationship between random matrix theory and symmetric spaces can be used in…

We investigate combinatorics of the instanton partition function for the generic four dimensional toric orbifolds. It is shown that the orbifold projection can be implemented by taking the inhomogeneous root of unity limit of the q-deformed…

We discuss N=2 supersymmetric quantum mechanics on the lattice using the fermion loop formulation. In this approach the system naturally decomposes into a bosonic and fermionic sector. This allows us to deal with the sign problem arising in…

In this paper we look at a class of random optimization problems that arise in the forms typically known in statistical physics as Little models. In \cite{BruParRit92} the Little models were studied by means of the well known tool from the…

An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…