相关论文: Replica Approach in Random Matrix Theory
In a series of recent scientific contributions the role of bosonic and fermionic ladder operators in a macroscopic realm has been investigated. Creation, annihilation and number operators have been used in very different contexts, all…
A subspace method is introduced to solve large-scale trace ratio problems. This approach is matrix-free, requiring only the action of the two matrices involved in the trace ratio. At each iteration, a smaller trace ratio problem is…
Simulations of supersymmetric field theories on the lattice with (spontaneously) broken supersymmetry suffer from a fermion sign problem related to the vanishing of the Witten index. We propose a novel approach which solves this problem in…
We review the ideas of how random matrix theory has to be properly applied to quantum physics; particularly we focus on how the spectrum has to be properly prepared and the random matrix correctly identified before the random matrix and the…
A recent paper by Jones-Smith and Mathur extends PT-symmetric quantum mechanics from bosonic systems (systems for which $T^2=1$) to fermionic systems (systems for which $T^2=-1$). The current paper shows how the formalism developed by…
The large-$N$ limit of $O(N)$-symmetric bosonic field theories, or $U(N)$-symmetric fermionic field theories, is amenable to a saddle point approximation. As a result, there is a family of closely related algorithms for efficient lattice…
Starting from Gaussian random matrix models we derive a new supermatrix field theory model. In contrast to the conventional non-linear sigma models, the new model is applicable for any range of correlations of the elements of the random…
We consider a new action of a two-dimensional field theory interacting with gravitational field. The action is interpreted as the area of a surface imbedded into four-dimensional Mincowski target space. In addition to reparametrization…
Since it was first applied to the study of nuclear interactions by Wigner and Dyson, almost 60 years ago, Random Matrix Theory (RMT) has developed into a field of its own within applied mathematics, and is now essential to many parts of…
This habilitation thesis summarizes the research that I have carried out from 2005 to 2019. It is organized in four chapters. The first three deal with random planar maps. Chapter 1 is about their metric properties: from a general…
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…
The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in con- junction of the replica method used to study thermodynamics properties of disordered…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
We consider certain scalar product of symmetric functions which is parameterized by a function $r$ and an integer $n$. One the one hand we have a fermionic representation of this scalar product. On the other hand we get a representation of…
A new approach to formulate the fermion field on lattice is introduced by proposing a new Dirac operator on lattice.This approach can eliminate the Fermion doubling problem, preserve the chiral symmetry and get the same dispersion relation…
The standard perturbation theory in QFT and lattice models leads to asymptotic expansions. However, an appropriate regularization of the path or lattice integrals allows one to construct convergent series with an infinite radius of the…
The partition function of the 2d Ising model with random nearest neighbor coupling is expressed in the dual lattice made of square plaquettes. The dual model is solved in the the mean field and in different types of Bethe-Peierls…
It is shown that supersymmetric integrable models in two dimensions, both relativistic (i.e. super-Toda type theories) and non-relativistic (reductions of super-KP hierarchies) can be associated to general Poisson-brackets structures given…
The supersymmetric method is a powerful method for the evaluation of quenched averages in disordered systems. Among others, this method has been applied to the theory of S-matrix fluctuations, the theory of universal conductance…
The four major asymptotic level density laws of random matrix theory may all be showcased though their Jacobi parameter representation as having a bordered Toeplitz form. We compare and contrast these laws, completing and exploring their…