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July 2019 A general method for lower bounds on fluctuations of random variables
Sourav Chatterjee
Ann. Probab. 47(4): 2140-2171 (July 2019). DOI: 10.1214/18-AOP1304

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.

Citation

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Sourav Chatterjee. "A general method for lower bounds on fluctuations of random variables." Ann. Probab. 47 (4) 2140 - 2171, July 2019. https://doi.org/10.1214/18-AOP1304

Information

Received: 1 August 2017; Revised: 1 July 2018; Published: July 2019
First available in Project Euclid: 4 July 2019

zbMATH: 07114713
MathSciNet: MR3980917
Digital Object Identifier: 10.1214/18-AOP1304

Subjects:
Primary: 60B20, 60C05, 60E15, 60K35

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 4 • July 2019
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