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An exact solution for a simple reaction-diffusion lattice model

Mathematical Physics & Probability

Speaker: Arvind Ayyer, Institut de Physique Theorique CEA Saclay
Location: 1147 MSB
Start time: Wed, Jun 2 2010, 4:10PM

Inspired by the border process of Glauber dynamics in the one dimensional Ising model, we consider a nonequilibrium exclusion process on a finite open lattice with both hopping and annihilation rates. The process is defined as a Markov chain. We obtain the steady state distribution of the chain exactly for any finite size using a new approach that we call the "transfer matrix ansatz". We also calculate physical quantities such as the "partition function", densities and two-point functions in this model. Lastly, we had an explicit conjecture for all the eigenvalues of the corresponding transition matrix, which was proven subsequently by Volker Strehl. This is joint work with Kirone Mallick.