Article

Probability Theory and Related Fields

, Volume 130, Issue 3, pp 289-318

Critical resonance in the non-intersecting lattice path model

  • Richard W. KenyonAffiliated withCNRS UMR 8628, Laboratoire de Mathématiques, Université Paris-Sud
  • , David B. WilsonAffiliated withMicrosoft Research, One Microsoft Way Email author 

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Abstract.

We study the phase transition in the honeycomb dimer model (equivalently, monotone non-intersecting lattice path model). At the critical point the system has a strong long-range dependence; in particular, periodic boundary conditions give rise to a “resonance” phenomenon, where the partition function and other properties of the system depend sensitively on the shape of the domain.