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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Markov Chains and θ-Congruent Number Problem
马尔可夫链 θ-同余数 θ-全等数分布
2023/5/10
A positive integer n is called a θ-congruent number if n sin θ is the area of a triangle with rational side lengths and with an angle θ. Markov chains play a key role in the study of the distribution ...
A Gaussian upper bound for the iterated kernels of Markov chains is obtained under some natural conditions. This result applies in particular to simple random walks on any locally compact unimodular g...
Fastest mixing Markov chain on a path
Random walks symmetrical transition probability markov chain the uniform distribution the transfer matrix
2015/8/10
We consider a random walk on a path with n nodes, with symmetric transition probabilities, i.e., the probability of making a transition between node i and node i+1 is the same as making a transition f...
Chutes and Ladders in Markov Chains
Markov chains stationary distribution Bessel diffusions Sierspinski gasket
2015/7/14
We investigate how the stationary distribution of a Markov chain changes when
transitions from a single state are modified. In particular, adding a single
directed edge to nearest neighbor random wa...
ANALYSIS OF A BOSE-EINSTEIN MARKOV CHAIN
Convergence rate markov chain stationarity k arcsine
2015/7/8
This paper gives sharp rates of convergence to stationarity for a Markov chain generating Bose-Einstein configurations of n balls in k boxes. The analysis leads to curious identities for the arc...
Fastest mixing Markov chain on a path
Distribution probability the edge markov chain random walk
2015/7/8
We consider the problem of assigning transition probabilities to the edges of a path, so the resulting Markov chain or random walk mixes as rapidly as possible. In this note we prove that fastest mixi...
The Fastest Mixing Markov Process on a Graph and a Connection to a Maximum Variance Unfolding Problem
Markov connected graph edge tags transition rates
2015/7/8
We consider a Markov process on a connected graph, with edges labeled with transition rates between the adjacent vertices. The distribution of the Markov process converges to the uniform distribution ...
Regular perturbation of V -geometrically ergodic Markov chains
Regular perturbation V -geometrically ergodic Markov chains Probability
2012/6/21
In this paper, new conditions for the stability of V-geometrically ergodic Markov chains are introduced. The results are based on an extension of the standard perturbation theory formulated by Keller ...
Cover times for sequences of Markov chains on random graphs
Random walk Cover time Maximal hitting time Random graph
2012/6/15
We provide conditions that classify cover times for sequences of random walks on random graphs into two types: One type (type 1) is the class of cover times approximated by the maximal hitting times s...
Tunneling and Metastability of continuous time Markov chains II, the nonreversible case
Metastability Tunneling Markov processes
2012/5/25
We proposed in \cite{bl2} a new approach to prove the metastable behavior of reversible dynamics based on potential theory and local ergodicity. In this article we extend this theory to nonreversible ...
Ruin theory with a Markov chain interest model
Probability Markov chain Ruin function Interest
2011/11/5
In this paper we consider a discrete time risk process with a Markov chain interest model. We derive recursive equations satisfied respectively by the joint distribution of surplus immediately before ...
Upper Bounds for Markov Approximations of Ergodic Processes
Chains of infinite order coupling from the past algorithms canonical Markov approximation d-distance Kullback-Leibler divergence
2011/9/19
Abstract: Chains of infinite order are generalizations of Markov chains that constitute a flexible class of models in the general theory of stochastic processes. These processes can be naturally studi...
Commuting time geometry of ergodic Markov chains
Commuting time geometry ergodic Markov chains Probability
2011/9/5
Abstract: We show how to map the states of an ergodic Markov chain to Euclidean space so that the squared distance between states is the expected commuting time. We find a minimax characterization of ...
Branching Markov processes on fragmentation trees generated from the paintbox process
Branching Markov processes fragmentation trees the paintbox process Probability
2011/9/5
Abstract: A fragmentation of a set $A$ is a graph with vertices labeled by subsets of $A$ which obey a certain parent-child relationship. A random fragmentation tree is a probability distribution on t...
A consistent Markov partition process generated from the paintbox process
paintbox process Ewens partition Poisson-Dirichlet distribution partition process
2011/9/5
Abstract: We study a family of Markov processes on $\mathcal{P}^{(k)}$, the space of partitions of the natural numbers with at most $k$ blocks. The process can be constructed from a Poisson point proc...