The main subject of the thesis is concerned with interacting particle systems, which are classes of spatio-temporal stochastic processes describing the evolution of particles in interaction with each other. The particles move on a finite or infinite discrete space and on each element of this space the state of the configuration is integer valued. Configurations of particles evolve in continuous time according to a Markov process. Here the space is either the infinite deterministic d-dimensional lattice or a random graph given by the finite d-dimensional torus with random matchings. In Part I we investigate the stochastic order in a particle system with multiple births, deaths and jumps on the d-dimensional lattice: stochastic order is a key tool to understand the ergodic properties of a system. We give applications on biological models of spread of epidemics and metapopulation dynamics systems. In Part II we analyse the coalescing random walk in a class of finite random graphs modeling social networks, the small world graphs. We derive the law of the meeting time of two random walks on small world graphs and we use this result to understand the role of random connections in meeting time of random walks and to investigate the behavior of coalescing random walks.

(2009). Interacting particle systems: stochastic order, attractiveness and random walks on small world graphs. (Tesi di dottorato, Università degli Studi di Milano-Bicocca, 2009).

Interacting particle systems: stochastic order, attractiveness and random walks on small world graphs

BORRELLO, DAVIDE
2009-12-03

Abstract

The main subject of the thesis is concerned with interacting particle systems, which are classes of spatio-temporal stochastic processes describing the evolution of particles in interaction with each other. The particles move on a finite or infinite discrete space and on each element of this space the state of the configuration is integer valued. Configurations of particles evolve in continuous time according to a Markov process. Here the space is either the infinite deterministic d-dimensional lattice or a random graph given by the finite d-dimensional torus with random matchings. In Part I we investigate the stochastic order in a particle system with multiple births, deaths and jumps on the d-dimensional lattice: stochastic order is a key tool to understand the ergodic properties of a system. We give applications on biological models of spread of epidemics and metapopulation dynamics systems. In Part II we analyse the coalescing random walk in a class of finite random graphs modeling social networks, the small world graphs. We derive the law of the meeting time of two random walks on small world graphs and we use this result to understand the role of random connections in meeting time of random walks and to investigate the behavior of coalescing random walks.
BERTACCHI, DANIELA
SAADA, ELLEN
Interacting particle systems; Attractiveness, Stochastic order; Metapopulation dynamics models; Allee effect; Mass migration; Small world graphs; Hitting time of random walks; Coalescing random walk
MAT/06 - PROBABILITA E STATISTICA MATEMATICA
English
Scuola di dottorato di Scienze
MATEMATICA PURA E APPLICATA - 23R
22
2008/2009
(2009). Interacting particle systems: stochastic order, attractiveness and random walks on small world graphs. (Tesi di dottorato, Università degli Studi di Milano-Bicocca, 2009).
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/7467
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