# Duke Probability Seminar

### A seminar for the probability community at Duke, both in and outside of the Mathematics Department.

#### More information on the Duke Probability community can be found on the Probability: Theory and Applications Page

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Upcoming Seminars:
• Thursday, September 26, 2019, 3:15pm, 119 Physics, Probability Seminar
Branching diffusion processes in periodic media
Pratima Hebbar (Duke)

We investigate the asymptotic behavior of solutions to parabolic partial differential equations (PDEs) in R^d with space-periodic diffusion matrix, drift, and potential. Using this asymptotics, we describe the behavior of branching diffusion processes in periodic media. In particular, for a super-critical branching process in periodic media, we distinguish two types of behavior for the normalized number of particles in a bounded domain, depending on the distance of the domain from the region where the bulk of the particles is located. At distances that grow linearly in time, we observe intermittency (i.e., the k−th moment dominates the k−th power of the first moment for some k), while, at distances that grow sub-linearly in time, we show that all the moments converge.

• Thursday, October 17, 2019, 3:15pm, 119 Physics, Probability Seminar
TBA
Mackenzie Simper (Stanford statistics)

• Thursday, October 24, 2019, 3:15pm, 119 Physics, Probability Seminar
Constructing extremal stationary distributions for the Voter Model in $d\geq 3$ as factors of IID
Lingfu Zhang (Princeton)

The Voters Model in $\mathbb{Z}^d$ lattice is a well studied interacting particle system. For $d \geq 3$, it has a one parameter family of extremal stationary distributions. Steif and Tykesson asked if these stationary distributions are factors of IID, or equivalently, isomorphic to Bernoulli shifts. We give an affirmative answer to this question. Our result also gives the first natural example of the so-called divide and color models, such that each cluster of the partition is infinite, while the coloring process is a factor of IID. It is a joint work with Allan Sly.

• Thursday, October 31, 2019, 3:15pm, 119 Physics, Probability Seminar