May
17
3:20pm 3:20pm

Asymptotic Fluctuations for Random Integer Partitions

Zhonggen SU
Zhejiang University

Let n≥1 be a natural number, Pn a set of all integer partitions. To each partition λ assign a probability P (λ). Thus we have a finite probability space (Pn, P) and are interested in asymptotic behaviors of a typical partition under P as n→∞. In this talk we particularly focus on random multiplicative measure and Plancherel measure and study the asymptotic fluctuations of the boundary of a Young diagram around its limit shape. It turns out that we need to deal with two cases separately: at the edge and in the bulk. At the edge the fluctuations will asymptotically follow Gumbel and Tracy-Widom extremal laws, while in the bulk asymptotic normality holds.

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May
17
2:10pm 2:10pm

Path-valued Processes Associated with Tree-valued Processes

Zenghu LI
Beijing Normal University

A family of continuous-state branching processes is constructed as the solution flow of a jump-type stochastic equation system driven by time-space noises. The family can be regarded as an inhomogeneous increasing path-valued branching Markov process. Two nonlocal branching immigration super processes can be defined from the flow. We identify explicitly the branching mechanisms of those processes. The models give different formulations of the tree-valued Markov processes of Aldous and Pitman (1998) and Abraham and Delmas (2012).

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May
17
1:30pm 1:30pm

Self-adjoint Extensions, Point Potentials, and Pinned Polymers

Michael Cranston
University of California

In this talk we discuss closed self adjoint extensions of the Laplacian and fractional Laplacian on L^2 of Euclidean space minus the origin. In many cases there is a one parameter family of these operators that behave like the original operator plus a potential at the origin. Using these operators, we can construct polymer measures which exhibit interesting phase transitions from an extended state to a bound state where the pinning at the origin due to the potential takes over. The talk is based on joint works with Koralov, Molchanov, Squartini and Vainberg.

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May
17
10:50am10:50am

Contact Processes on Some Inhomogeneous Graphs and Random Graphs

Qiang YAO
East China Normal University

The study of stochastic processes in inhomogeneous environments and random environments is developing well in probability theory. In this talk I first briefly review some basic facts on contact processes. Then I introduce some previous models on contact processes in inhomogeneous environments and random environments. Finally, I report some recent works on contact processes on some inhomogeneous graphs and random graphs. Some basic ideas of the proofs are given. (The talk is based on some joint works with Xinxing Chen, Thomas Mountford, Jean-Christophe Mourrat and Daniel Valesin.)

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May
17
9:00am 9:00am

Predictability in Nonequilibrium Discrete Spin Dynamics

Daniel Stein
New York University

Understanding the dynamical behavior of many-particle systems both in and out of equilibrium is a central issue in statistical mechanics. One question involves the relative importance of "nature vs. nurture" : that is, given a system with a random initial state evolving through a well-defined stochastic dynamics, how much of the information contained in the state at future times depends on the initial condition ("nature") and how much on the dynamical realization ("nurture")? I will discuss this question and present both old and new results for low-dimensional discrete spin systems.

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