Open Access
Geometric Random Walks: a Survey
Santosh Vempala
- pp 577-616
TLDR
In this paper, the developing theory of geometric random walks is outlined and general methods for estimating convergence (the mixinging rate), isoperimetric inequalities in R and their intimate connection to random walks are discussed.Abstract:
The developing theory of geometric random walks is outlined here. Three aspects—general methods for estimating convergence (the “mixing” rate), isoperimetric inequalities in R and their intimate connection to random walks, and algorithms for fundamental problems (volume computation and convex optimization) that are based on sampling by random walks—are discussed.read more
Citations
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Introduction to the non-asymptotic analysis of random matrices.
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MonographDOI
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References
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Journal ArticleDOI
Optimization by Simulated Annealing
TL;DR: There is a deep and useful connection between statistical mechanics and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters), and a detailed analogy with annealing in solids provides a framework for optimization of very large and complex systems.
Book
Geometric Algorithms and Combinatorial Optimization
TL;DR: In this article, the Fulkerson Prize was won by the Mathematical Programming Society and the American Mathematical Society for proving polynomial time solvability of problems in convexity theory, geometry, and combinatorial optimization.
Random Walks on Graphs: A Survey
TL;DR: Estimates on the important parameters of access time, commute time, cover time and mixing time are discussed and recent algorithmic applications of random walks are sketched, in particular to the problem of sampling.
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