• Corpus ID: 236635367

Asymptotic expansions for a class of Fredholm Pfaffians and interacting particle systems

  title={Asymptotic expansions for a class of Fredholm Pfaffians and interacting particle systems},
  author={Will FitzGerald and Roger Tribe and Oleg V. Zaboronski},
Motivated by the phenomenon of duality for interacting particle systems we introduce two classes of Pfaffian kernels describing a number of Pfaffian point processes in the ‘bulk’ and at the ‘edge’. Using the probabilistic method due to Mark Kac, we prove two Szegő-type asymptotic expansion theorems for the corresponding Fredholm Pfaffians. The idea of the proof is to introduce an effective random walk with transition density determined by the Pfaffian kernel, express the logarithm of the… 

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