Non-markov Property of Certain Eigenvalue Processes Analogous to Dyson’s Model
نویسندگان
چکیده
It is proven that the eigenvalue process of Dyson’s random matrix process of size two becomes non-Markov if the common coefficient 1/ √ 2 in the non-diagonal entries is replaced by a different positive number.
منابع مشابه
Noncolliding Brownian Motion and Determinantal Processes
A system of one-dimensional Brownian motions (BMs) conditioned never to collide with each other is realized as (i) Dyson’s BM model, which is a process of eigenvalues of hermitian matrixvalued diffusion process in the Gaussian unitary ensemble (GUE), and as (ii) the h-transform of absorbing BM in a Weyl chamber, where the harmonic function h is the product of differences of variables (the Vande...
متن کاملA Generalisation of Dyson’s Integration Theorem for Determinants
Dyson’s integration theorem is widely used in the computation of eigenvalue correlation functions in Random Matrix Theory. Here we focus on the variant of the theorem for determinants, relevant for the unitary ensembles with Dyson index β = 2. We derive a formula reducing the (n − k)-fold integral of an n × n determinant of a kernel of two sets of arbitrary functions to a determinant of size k×...
متن کاملApplication of Markov Processes to the Machine Delays Analysis
Production and non-productive equipment and personnel delays are a critical element of any production system. The frequency and length of delays impact heavily on the production and economic efficiency of these systems. Machining processes in wood industry are particularly vulnerable to productive and non-productive delays. Whereas, traditional manufacturing industries usually operate on homoge...
متن کاملA Model For The Residence Time Distribution and Holdup Measurement in a Two Impinging Streams Cyclone Reactor/Contactor in Solid-Liquid Systems
In this paper a two impinging streams cyclone contacting system suitable for handling of solid-liquid systems has been studied. Certain pertinent parameters such as: solid holdup, mean residence time and Residence Time Distribution (RTD) of solid particles have been investigated. A stochastic model based on Markov chains processes has been applied which describe the behavior of solid partic...
متن کاملMarkov Chains , Eigenvalues , and Coupling ( December
This is an expository paper which presents certain basic ideas related to nonasymptotic rates of convergence for Markov chains. In particular, we describe eigenvalue analysis, random walks on groups, coupling, and minorization conditions. Connections are made to modern areas of research, including analysis of card shuffling and analysis of stochastic algorithms used in statistics and computer s...
متن کامل