On transition matrices
نویسنده
چکیده
In the Conley index theory, transition matrices are used to detect bifurcations of codimension one connecting orbits in a Morse decomposition of an isolated invariant set. Here we shall give a new axiomatic definition of the transition matrix in order to treat several existing formulations of transition matrices in a unified manner.
منابع مشابه
Location Prediction Based on Transition Probability Matrices Constructing from Sequential Rules for Spatial-Temporal K-Anonymity Dataset
Spatial-temporal k-anonymity has become a mainstream approach among techniques for protection of users' privacy in location-based services (LBS) applications, and has been applied to several variants such as LBS snapshot queries and continuous queries. Analyzing large-scale spatial-temporal anonymity sets may benefit several LBS applications. In this paper, we propose two location prediction me...
متن کاملA phase transition for the limiting spectral density of random matrices ∗
We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated. Depending on the strength of correlation, the limiting spectral distribution is either the famous semicircle distribution, the distribution derived for Toep...
متن کاملProducts of Beta matrices and sticky flows
In [2], a family of stochastic flows of kernels on S 1 called " sticky flows " is described. Sticky flows are defined by their " moments " which are consistent systems of transition kernels on S 1. In this note, a discrete version of sticky flows is presented in the case the sticky flows are associated with a system of Brownian particles on S 1. This discrete model is defined by products of Bet...
متن کاملSharp Nonasymptotic Bounds on the Norm of Random Matrices with Independent Entries by Afonso
This bound is optimal in the sense that a matching lower bound holds under mild assumptions, and the constants are sufficiently sharp that we can often capture the precise edge of the spectrum. Analogous results are obtained for rectangular matrices and for more general subgaussian or heavy-tailed distributions of the entries, and we derive tail bounds in addition to bounds on the expected norm...
متن کاملar X iv : 0 90 7 . 45 02 v 1 [ m at h . PR ] 2 6 Ju l 2 00 9 On Markov chains induced by partitioned transition probability matrices
Let S be a denumerable state space and let P be a transition probability matrix on S. If a denumerable set M of nonnegative matrices is such that the sum of the matrices is equal to P , then we call M a partition of P . Let K denote the set of probability vectors on S. To every partition M of P we can associate a transition probability function PM on K defined in such a way that if p ∈ K and M ...
متن کامل