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A Convexity Property of Discrete Random Walks

Part of: Stochastic processes Markov processes Geometric function theory

Published online by Cambridge University Press:  31 March 2016

GÁBOR V. NAGY  and
VILMOS TOTIK
GÁBOR V. NAGY
Affiliation:
Bolyai Institute, University of Szeged, Szeged, Aradi v. tere 1, 6720, Hungary (e-mail: ngaba@math.u-szeged.hu)
VILMOS TOTIK
Affiliation:
MTA-SZTE Analysis and Stochastics Research Group, Bolyai Institute, University of Szeged, Szeged, Aradi v. tere 1, 6720, Hungary and Department of Mathematics and Statistics, University of South Florida, 4202 E. Fowler Ave, CMC342, Tampa, FL 33620-5700, USA (e-mail: totik@mail.usf.edu)
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Abstract

We establish a convexity property for the hitting probabilities of discrete random walks in ${\mathbb Z}^d$ (discrete harmonic measures). For d = 2 this implies a recent result on the convexity of the density of certain harmonic measures.

MSC classification

Primary: 60J45: Probabilistic potential theory
Secondary: 60G50: Sums of independent random variables; random walks 30C85: Capacity and harmonic measure in the complex plane
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 25 , Issue 6 , November 2016 , pp. 928 - 940
Copyright
Copyright © Cambridge University Press 2016 

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