Dualitiy, bosonic particle systems and some exactly solvable models of non-equilibrium

Vafayi, K. (2011)

Doctoral Thesis

We study stochastic models of non-equilibrium which are exactly solvable with the technique of duality and self-duality. The models include a new class of particle systems which are bosonic, i.e., models where there is an attractive interaction between the particles and as a consequence condensation phenomena can occur. Our models belong to the class of interacting particle systems, or systems of interacting diffusions. Via the technique of duality, we connect models of interacting diffusions (e.g. Brownian Momentum Process) to simpler interacting particle systems (e.g. Symmetric Inclusion Process), both in equilibrium and non-equilibrium settings. Part of the thesis is devoted to develop a general formalism for duality.

• Non-equilibrium statistical mechanics
• Symmetric inclusion process
• Duality
• Interacting particle systems
• Heat conduction models
• Weak coupling limit
• Condensation
• Correlation inequalities

• All authors: Vafayi, K.
• Supervisor: Redig, F.H.J.
• Co-supervisor: Hollander, W.T.F. den
• Qualification: Doctor (dr.)
• Awarding Institution: Faculty of Science, Leiden University
• Date: 2011-12-13