# 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, November 5, 2020, 3:15pm, Virtual, Probability Seminar
Critical One-dimensional Multi-particle DLA
Danny Nam (Princeton, math)

In multi-particle Diffusion Limited Aggregation (DLA) a sea of particles performs independent random walks until they run into the aggregate and are absorbed. In dimension 1, the rate of growth of the aggregate depends on $\lambda$, the density of the particles. Kesten and Sidoravicius proved that when $\lambda < 1$ the aggregate grows like $t^{1/2}$. They furthermore predicted linear growth when $\lambda > 1$ (subsequently confirmed by Sly) and $t^{2/3}$ growth at the critical density $\lambda = 1$. We address the critical case, confirming the $t^{2/3}$ growth and show that aggregate has a scaling limit whose derivative is a self-similar diffusion. Surprisingly, this contradicts conjectures on the speed in the mildly supercritical regime when $\lambda = 1 + \epsilon$. Email Jim Nolen (nolen@math.duke.edu) for the zoom link.

• Thursday, November 12, 2020, 3:15pm, Virtual, Probability Seminar
Approximating Quasi-Stationary Distributions with Interacting Reinforced Random Walks

We propose two numerical schemes for approximating quasi-stationary distributions (QSD) of finite state Markov chains with absorbing states. Both schemes are described in terms of certain interacting chains in which the interaction is given in terms of the total time occupation measure of all particles in the system. The schemes can be viewed as combining the key features of the two basic simulation-based methods for approximating QSD originating from the works of Fleming and Viot (1979) and Aldous, Flannery, and Palacios (1998), respectively. In this talk I will describe the two schemes, discuss their convergence properties, and present some exploratory numerical results comparing them to other QSD approximation methods. Email Jim Nolen (nolen@math.duke.edu) for the zoom link.

• Monday, November 16, 2020, 3:30pm, Zoom link, Probability Seminar
TBA
Kavita Ramnan (Brown, applied math)

• Thursday, November 19, 2020, 3:15pm, Virtual, Probability Seminar
K-means clustering with optimization