Abstract:
Consider a statistical physical model on the infinite d-regular tree Td described by a set of interactions Φ. Let {Gn} be a sequence of finite d-regular graphs with vertex sets Vn that locally converge to Td. From Φ, one can construct a sequence of corresponding Gibbs measures {μn}n∈N on the graphs Gn. Here we assume that {μn} converges to some limiting Gibbs measure μ on Td in the local weak sense. We show that the limit supremum of |Vn|-1 H(μn) is bounded above by the percolative entropy Hperc(μ), a function of μ itself, and that |Vn|-1H(μn) actually converges to Hperc(μ) when Φ exhibits strong spatial mixing on Td. When it is known to exist, the limit of |Vn|-1H(μn) is most commonly shown to be given by the Bethe ansatz. Percolative entropy gives a different formula, and we do not know how to connect it to the Bethe ansatz directly. Joint work with Tim Austin, University of California, Los Angeles.
Biography:
Moumanti Podder is a Postdoctoral Fellow (Acting Assistant Professor) at the University of Washington. She completed her Bachelors and Masters in Statistics at the Indian Statistical Institute, Kolkata, before moving to the United States to pursue her Ph.D. in Mathematics at the Courant Institute of Mathematical Sciences, New York University, under the advisement of Joel Spencer (Ph.D. awarded 2017). Before starting at the University of Washington, she was a Postdoctoral Fellow for one year at the Georgia Institute of Technology's School of Mathematics, working with the Discrete Mathematics group. She is interested in random graphs, especially Galton-Watson trees, on which she studies probabilities of properties expressed as mathematical logical sentences, in studying statistical physical models on regular trees or finite trees of bounded degree, in problems of interacting particle systems etc.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai