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Persistence Probability for a Class of Gaussian Processes Related to Random Interface Models

Part of: Stochastic processes Special processes Time-dependent statistical mechanics (dynamic and nonequilibrium)

Published online by Cambridge University Press:  04 January 2016

Hironobu Sakagawa
Hironobu Sakagawa*
Affiliation:
Keio University
*
∗ Postal address: Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kouhoku-ku, Yokohama, 223-8522, Japan. Email address: sakagawa@math.keio.ac.jp
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Abstract

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We consider a class of Gaussian processes which are obtained as height processes of some (d + 1)-dimensional dynamic random interface model on ℤd. We give an estimate of persistence probability, namely, large T asymptotics of the probability that the process does not exceed a fixed level up to time T. The interaction of the model affects the persistence probability and its asymptotics changes depending on the dimension d.

Keywords

Persistence probabilityrandom interfaceGaussian processinteracting diffusion process

MSC classification

Primary: 60G15: Gaussian processes
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory 82C41: Dynamics of random walks, random surfaces, lattice animals, etc.
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 47 , Issue 1 , March 2015 , pp. 146 - 163
Copyright
© Applied Probability Trust 

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