Related papers: Determinism plus chance in random matrix theory
A Hamiltonian analysis of models given by a three-form field with a generic potential coupled to general relativity in four dimensions is performed. This kind of fields are naturally present in string theory and cosmological scenarios. In…
Maximum likelihood estimation is a fundamental optimization problem in statistics. We study this problem on manifolds of matrices with bounded rank. These represent mixtures of distributions of two independent discrete random variables. We…
The nonequilibrium dynamics in chaotic quantum systems denies a fully understanding up to now, even if thermalization in the long-time asymptotic state has been explained by the eigenstate thermalization hypothesis which assumes a universal…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
We study a system of $N$ qubits with a random Hamiltonian obtained by drawing coupling constants from Gaussian distributions in various ways. This results in a rich class of systems which include the GUE and the fixed $q$ SYK theories. Our…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…
Deterministic simulations of the rate equations governing cluster dynamics in materials are limited by the number of equations to integrate. Stochastic simulations are limited by the high frequency of certain events. We propose a coupling…
In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…
The ensemble inter-relations to be considered are special features of classical cases, where the joint eigenvalue probability density can be computed explicitly. Attention will be focussed too on the consequences of these inter-relations,…
This work introduces a novel probabilistic deep learning technique called deep Gaussian mixture ensembles (DGMEs), which enables accurate quantification of both epistemic and aleatoric uncertainty. By assuming the data generating process…
The spectral density of random matrices is studied through a quaternionic generalisation of the Green's function, which precisely describes the mean spectral density of a given matrix under a particular type of random perturbation. Exact…
Connectivity estimation is challenging in the context of high-dimensional data. A useful preprocessing step is to group variables into clusters, however, it is not always clear how to do so from the perspective of connectivity estimation.…
We consider how to describe Hamiltonian mechanics in generalised probabilistic theories with the states represented as quasi-probability distributions. We give general operational definitions of energy-related concepts. We define…
The generalized density matrix (GDM) method is used to calculate microscopically the parameters of the collective Hamiltonian. Higher order anharmonicities are obtained consistently with the lowest order results, the mean field…
We show that the relativistic energy-momentum relation can emerge as an effective ensemble-averaged structure from a multiplicative Hamiltonian when fluctuations of an auxiliary parameter are treated using maximum entropy inference. The…
We develop Hamiltonian formalism for Lagrange Multiplier Modified Gravity. We further calculate the Poisson brackets between constraints and we show that they coincide with the algebra of constraints in Hamiltonian formulation of General…
In this paper we present a unifying geometric and compositional framework for modeling complex physical network dynamics as port-Hamiltonian systems on open graphs. Basic idea is to associate with the incidence matrix of the graph a Dirac…
The main goal of these lectures is to introduce and review the Hamiltonian formalism for classical constrained systems and in particular gauge theories. Emphasis is put on the relation between local symmetries and constraints and on the…
We use a Hamiltonian (transition matrix) description of height-restricted Dyck paths on the plane in which generating functions for the paths arise as matrix elements of the propagator to evaluate the length and area generating function for…