A general method for lower bounds on fluctuations of random variables
Probability
2018-07-30 v3 Combinatorics
Abstract
There are many ways of establishing upper bounds on fluctuations of random variables, but there is no systematic approach for lower bounds. As a result, lower bounds are unknown in many important problems. This paper introduces a general method for lower bounds on fluctuations. The method is used to obtain new results for the stochastic traveling salesman problem, the stochastic minimal matching problem, the random assignment problem, the Sherrington-Kirkpatrick model of spin glasses, first-passage percolation and random matrices. A long list of open problems is provided at the end.
Cite
@article{arxiv.1706.04290,
title = {A general method for lower bounds on fluctuations of random variables},
author = {Sourav Chatterjee},
journal= {arXiv preprint arXiv:1706.04290},
year = {2018}
}
Comments
32 pages. Additional references in this revision, and a note about a connection with the Mermin-Wagner theorem. To appear in the Annals of Probability