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Terry Soo

  1. Weak mixing suspension flows over shifts of finite type are universal.

    Пт, 10/07/2011 - 15:01 — SomNambul
    Authors: Terry Soo, Anthony Quas
    Subjects: Dynamical Systems
    Abstract

    Let S be an ergodic measure-preserving automorphism on a non-atomic
    probability space, and let T be the time-one map of a topologically weak mixing
    suspension flow over an irreducible subshift of finite type under a Holder
    ceiling function. We show that if the measure-theoretic entropy of the S is
    strictly less than the topological entropy of T, then there exists an embedding
    from the measure-preserving automorphism into the suspension flow.

  2. Deterministic Thinning of Finite Poisson Processes.

    Ср, 12/02/2009 - 16:01 — SomNambul
    Authors: Alexander E. Holroyd, Terry Soo, Omer Angel
    Subjects: Probability
    Abstract

    Let Pi and Gamma be homogeneous Poisson point processes on a fixed set of
    finite volume. We prove a necessary and sufficient condition on the two
    intensities for the existence of a coupling of Pi and Gamma such that Gamma is
    a deterministic function of Pi, and all points of Gamma are points of Pi. The
    condition exhibits a surprising lack of monotonicity. However, in the limit of
    large intensities, the coupling exists if and only if the expected number of
    points is at least one greater in Pi than in Gamma.

  3. Poisson Splitting by Factors.

    Втр, 08/25/2009 - 22:41 — SomNambul
    Authors: Alexander E. Holroyd, Russell Lyons, Terry Soo
    Subjects: Probability
    Abstract

    Given a homogeneous Poisson process on R^d with intensity L, we prove that it
    is possible to partition the points into two sets, as a deterministic function
    of the process, and in an isometry-equivariant way, so that each set of points
    forms a homogeneous Poisson process, with any given pair of intensities summing
    to L. In particular, this answers a question of Ball, who proved that in d=1,
    the Poisson points may be similarly partitioned (via a translation-equivariant
    function) so that one set forms a Poisson process of lower intensity, and asked
    whether the same was possible for all d.

Math-arch

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