We prove the Bernoulli property for determinantal point processes on with translation-invariant kernels. For the determinantal point processes on with translation-invariant kernels, the Bernoulli property was proved by Lyons and Steif [Stationary determinantal processes: Phase multiplicity, bernoullicity, and domination. Duke Math. J. 120 (2003), 515-575] and Shirai and Takahashi [Random point fields associated with certain Fredholm determinants II: Fermion shifts and their ergodic properties. Ann. Probab. 31 (2003), 1533-1564]. We prove its continuum version. For this purpose, we also prove the Bernoulli property for the tree representations of the determinantal point processes.
All Science Journal Classification (ASJC) codes
- Applied Mathematics