Philippe Biane

Norio Konno

Fabio Cipriani

Luc Bouten

Quanhua Xu

This book offers the revised and completed notes of lectures given at the 2007 conference, "Quantum Potential Theory: Structures and Applications to Physics." These lectures provide an introduction to the theory and discuss various applications.

Quantum Potential Theory

Recently, interacting particle systems have been studied widely from the standpoints of mathematics, physics, chemistry and biology. Many researchers are becoming interested in this field. This book focuses on the phase transitions of interacting particle systems, especially their critical values and order parameters. It poses the following question: How can we get good bounds on the critical values and the order parameters? This question is very basic, and many researchers have been trying to get better bounds rigorously. Hence the book provides bounds — both the author's and others'. Contents:Introduction — Markov ChainsContact Process Type Models on Small Finite SetsThe Basic Contact ProcessThe θ-Contact ProcessDiffusive Contact ProcessesLong Range Contact ProcessesUniform Nearest-Particle SystemsParticle Systems on Trees Readership: Probabilists, mathematical physicists, statistical physicists and mathematical biologists. keywords:Phase Transition;Interacting Particle System;Critical Value;Order Parameter;Contact Process;Nearest Particle System;Correlation Inequality;Bounds;Duality;Correlation Identities

Norio Konno

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