Random generation of combinatorial structures from a uniform
Theoretical Computer Science
Time to reach stationarity in the Bernoulli-Laplace diffusion model
SIAM Journal on Mathematical Analysis
Conductance and the rapid mixing property for Markov chains: the approximation of permanent resolved
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Elements of information theory
Elements of information theory
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
Faster mixing via average conductance
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Spectral Gap and log-Sobolev Constant for Balanced Matroids
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Torpid Mixing of Some Monte Carlo Markov Chain Algorithms in Statistical Physics
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Simulated Annealing in Convex Bodies and an 0*(n4) Volume Algorithm
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
Journal of the ACM (JACM)
Fastest Mixing Markov Chain on a Graph
SIAM Review
Approximately counting integral flows and cell-bounded contingency tables
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Vertex and edge expansion properties for rapid mixing
Random Structures & Algorithms - Proceedings of the Eleventh International Conference "Random Structures and Algorithms," August 9—13, 2003, Poznan, Poland
Rapidly Mixing Markov Chains with Applications in Computer Science and Physics
Computing in Science and Engineering
SIAM Journal on Computing
Blocking Conductance and Mixing in Random Walks
Combinatorics, Probability and Computing
The Mixing Time of the Thorp Shuffle
SIAM Journal on Computing
Spectral analysis of pollard rho collisions
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Detecting Overlapping Community Structures in Networks
World Wide Web
Foundations and Trends® in Networking
Using Histograms to Better Answer Queries to Probabilistic Logic Programs
ICLP '09 Proceedings of the 25th International Conference on Logic Programming
On the isoperimetric spectrum of graphs and its approximations
Journal of Combinatorial Theory Series B
Forward-secure key evolution in wireless sensor networks
CANS'07 Proceedings of the 6th international conference on Cryptology and network security
Approximations for the isoperimetric and spectral profile of graphs and related parameters
Proceedings of the forty-second ACM symposium on Theory of computing
Information theoretic bounds for distributed computation over networks of point-to-point channels
IEEE Transactions on Information Theory
Distributed random access algorithm: scheduling and congestion control
IEEE Transactions on Information Theory
The mixing time of the Newman: Watts small world
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Spectral analysis of pollard rho collisions
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Identifying community structures in networks with seed expansion
DASFAA'10 Proceedings of the 15th international conference on Database Systems for Advanced Applications - Volume Part I
Erdős-Rényi sequences and deterministic construction of expanding cayley graphs
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Focused most probable world computations in probabilistic logic programs
Annals of Mathematics and Artificial Intelligence
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In the past few years we have seen a surge in the theory of finite Markov chains, by way of new techniques to bounding the convergence to stationarity. This includes functional techniques such as logarithmic Sobolev and Nash inequalities, refined spectral and entropy techniques, and isoperimetric techniques such as the average and blocking conductance and the evolving set methodology. We attempt to give a more or less self-contained treatment of some of these modern techniques, after reviewing several preliminaries. We also review classical and modern lower bounds on mixing times. There have been other important contributions to this theory such as variants on coupling techniques and decomposition methods, which are not included here; our choice was to keep the analytical methods as the theme of this presentation. We illustrate the strength of the main techniques by way of simple examples, a recent result on the Pollard Rho random walk to compute the discrete logarithm, as well as with an improved analysis of the Thorp shuffle.