相关论文: New Developments In Non-Hermitian Random Matrix Mo…

Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…

We establish a precise three-term asymptotic expansion, with an optimal estimate of the error term, for the rightmost eigenvalue of an $n\times n$ random matrix with independent identically distributed complex entries as $n$ tends to…

The non-Hermitian formalism is used at present in many papers for the description of open quantum systems. A special language developed in this field of physics which makes it difficult for many physicists to follow and to understand the…

Duality identities in random matrix theory for products and powers of characteristic polynomials, and for moments, are reviewed. The structure of a typical duality identity for the average of a positive integer power $k$ of the…

We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It…

In principle, non-Hermitian quantum equations of motion can be formulated using as a starting point either the Heisenberg's or the Schr\"odinger's picture of quantum dynamics. Here it is shown in both cases how to map the algebra of…

We establish formulae for the moments of the moments of the characteristic polynomials of random orthogonal and symplectic matrices in terms of certain lattice point count problems. This allows us to establish asymptotic formulae when the…

The paper is devoted to a study of phase transitions in the Hermitian random matrix models with a polynomial potential. In an alternative equivalent language, we study families of equilibrium measures on the real line in a polynomial…

Non-hermitian systems have gained a lot of interest in recent years. However, notions of chaos and localization in such systems have not reached the same level of maturity as in the Hermitian systems. Here, we consider non-hermitian…

We define a random commuting $d$-tuple of $n$-by-$n$ matrices to be a random variable that takes values in the set of commuting $d$-tuples and has a distribution that is a rapidly decaying continuous weight on this algebraic set. In the…

Unitarity is a cornerstone of quantum theory, ensuring the conservation of probability and information. Although non-Hermitian Hamiltonians are typically associated with open or dissipative systems, pseudo-Hermitian quantum mechanics shows…

Moments of secular and inverse secular coefficients, averaged over random matrices from classical groups, are related to the enumeration of non-negative matrices with prescribed row and column sums. Similar random matrix averages are…

A non-supersymmetric grand unified theory can exhibit a "radiative fermion mass hierarchy", in which the heavier quarks and leptons get mass at tree level and the lighter ones get mass from loop diagrams. Recently the first predictive model…

We characterize asymptotic collective behaviour of rectangular random matrices, the sizes of which tend to infinity at different rates: when embedded in a space of larger square matrices, independent rectangular random matrices are…

In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of…

The dynamical and topological properties of non-Hermitian systems have attracted great attention in recent years. In this work, we establish an intrinsic connection between two classes of intriguing phenomena -- topological phases and…

Neural network models are one of the most successful approaches to machine learning, enjoying an enormous amount of development and research over recent years and finding concrete real-world applications in almost any conceivable area of…

We explore the probability that a permutation sampled from the symmetric group of order n uniformly at random has cycles of lengths not exceeding r. Asymptotic formulas valid in specified regions for the ratio n/r are obtained using the…

We use the Riemann-Hilbert approach, together with string and Toda equations, to study the topological expansion in the quartic random matrix model. The coefficients of the topological expansion are generating functions for the numbers…

Recent years have seen a growing interest in topological phases beyond the standard paradigm of gapped, isolated systems. One recent direction is to explore topological features in non-hermitian systems that are commonly used as effective…