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Lie algebraic constructions of particle systems

  • Date May 2, 2017
  • Hour 3 pm
  • Room GSSI Library Room
  • Speaker Frank Redig (TU - DELFT)

ABSTRACT

We describe a general Lie-algebraic method to construct stochastic interacting particle systems with symmetries, i.e., operators commuting with the generator. As a consequence, such processes have automatically self-duality properties. We illustrate this for the particle systems of the so-called SIP family (symmetric inclusion process) which stems from the algebra SU(1,1) and contains a discrete particle hopping system, an interacting diffusion process, and an energy redistribution model of KMP type. We also describe how to find the "correct" asymmetric analogues of these models by a deformation of the corresponding algebra. (Based on joint work with Gioia Carinci, Cristian Giardina and Tomohiro Sasamoto).