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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
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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 ...
Complexity of Estimating Renyi Entropy of Markov Chains
information theory Renyi entropy Min-entropy
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2019/7/8
Estimating entropy of random processes is one of the fundamental problems of machine learning and property testing. It has numerous applications to anything from DNA testing and predictability of huma...
LINGUISTIC CRACKING OF PASSPHRASES USING MARKOV CHAINS
Passphrases Cracking Markov chains
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2016/3/7
In order to remember long passwords, it is not uncommon users are recommended to create a sentence which then is assembled to form a long password, a passphrase. However, theoretically a language is v...
Overshoot in biological systems modeled by Markov chains: a nonequilibrium dynamic phenomenon
Overshoot adaptation Markov chains net flux oscillation nonequilibrium
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2016/1/26
A number of biological systems can be modeled by Markov chains. Recently, there has been an increasing concern about when biological systems modeled by Markov chains will perform a dynamic phenomenon ...
Overshoot in biological systems modeled by Markov chains:a nonequilibrium dynamic phenomenon
Overshoot adaptation Markov chains net flux oscillation nonequilibrium
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2016/1/20
A number of biological systems can be modeled by Markov chains. Recently, there has been an increasing concern about when biological systems modeled by Markov chains will perform a dynamic phenomenon ...
Nash Inequalities for Finite Markov Chains
Finite Markov Chains Inequalities
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2015/8/26
This paper develops bounds on the rate of decay of powers of Markov kernels
on finite state spaces. These are combined with eigenvalue estimates to give
good bounds on the rate of convergence to sta...
LOGARITHMIC SOBOLEV INEQUALITIES FOR FINITE MARKOV CHAINS
Sobolev inequality MARKOV CHAINS
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2015/8/26
This is an expository paper on the use of logarithmic Sobolev inequalities
for bounding rates of convergence of Markov chains on finite state
spaces to their stationary distributions. Logarithmic So...
COMPARISON THEOREMS FOR REVERSIBLE MARKOV CHAINS
MARKOV CHAINS COMPARISON THEOREMS
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2015/8/26
We introduce geometric comparison inequalities that give bounds on the eigenvalues of a reversible Markov chain in terms of the eigenvalues of a second chain. The bounds are applied to get sharp resul...
GAUSSIAN ESTIMATES FOR MARKOV CHAINS AND RANDOM WALKS ON GROUPS
GROUPS MARKOV CHAINS
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2015/8/26
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...
Symmetry analysis of reversible Markov chains
Reversible markov chain orbital diagram characteristic vector；the mixture of markov chain an arbitrary number
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2015/8/11
We show how to use subgroups of the symmetry group of a reversible Markov chain to give useful bounds on eigenvalues and their multiplicity. We supplement classical representation theoretic tools invo...
DE FINETTI'S THEOREM FOR MARKOV CHAINS
Markov chain the theorem
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2015/7/14
DE FINETTI'S THEOREM FOR MARKOV CHAINS.
Geometric Bounds for Eigenvalues of Markov Chains
Reversible markov chain geometry
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2015/7/14
We develop bounds for the second largest eigenvalue and spectral gap
of a reversible Markov chain. The bounds depend on geometric quantities
such as the maximum degree, diameter and covering numbe...
COMPARISON THEOREMS FOR REVERSIBLE MARKOV CHAINS
Geometry inequality reversible markov chain the characteristic value
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2015/7/14
We introduce geometric comparison inequalities that give bounds on
the eigenvalues of a reversible Markov chain in terms of the eigenvalues
of a second chain. The bounds are applied to get sharp r...
THREE EXAMPLES OF MONTE-CARLO MARKOV CHAINS:AT THE INTERFACE BETWEEN STATOSTICAL COMPUTING,COMPUTER SCIENCE,AND STATISTICAL MECHANICS
Monte carlo markov chain the interface between computing computer science statistical mechanics
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2015/7/14
THREE EXAMPLES OF MONTE-CARLO MARKOV CHAINS:AT THE INTERFACE BETWEEN STATOSTICAL COMPUTING,COMPUTER SCIENCE,AND STATISTICAL MECHANICS。
LOGARITHMIC SOBOLEV INEQUALITIES FOR FINITE MARKOV CHAINS
Logarithmic sobolev limited markov chain the inequality
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2015/7/14
LOGARITHMIC SOBOLEV INEQUALITIES FOR FINITE MARKOV CHAINS。