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- Thursday, January 30, 2020, 4:15pm, 119 Physics, Probability Seminar
*Asymptotic analysis of the power of choice phenomenon for queuing models*

Minheer Dewaskar (UNC, Statistics and Operations Research)- Suppose that n balls are to be sequentially placed into n bins with the objective of keeping the maximum load of the bins small. In absence of a central dispatcher, and in order to minimize the communication overhead, each incoming ball chooses d bins uniformly at random and goes into the bin with the smallest load among its d choices. The maximum bin load for d = 2 (or greater) is substantially smaller than that for d=1 : O(log log n) vs O(log n); this phenomenon is called the power of choice. The phenomenon is quite robust and has applications to large scale load balancing, hashing, collision protocols, etc. We will consider queuing models with load balancing undertaken using the above heuristic with the number of choices d \to \infty. Our aim is to develop mathematical techniques for both fluid limits and functional central limit theorems in various regimes of the model.

- Thursday, February 6, 2020, 4:15pm, at UNC, 125 Hanes Hall, Probability Seminar
*Sparse random graphs with overlapping community structure*

Samantha Petti (Georgia Tech)- In this talk we introduce two different random graph models that produce sparse graphs with overlapping community structure and discuss community detection in each context. The Random Overlapping Community (ROC) model produces a sparse graph by constructing many Erdos Renyi random graphs (communities) on small randomly selected subsets of vertices. By varying the size and density of these communities, ROC graphs can be tuned to exhibit a wide range normalized of closed walk count vectors, including those of hypercubes. This is joint work with Santosh Vempala. In the second half of the talk, we introduce the Community Configuration Model (CCM), a variant of the configuration model in which half-edges are assigned colors and pair according to a matching rule on the colors. The model is a generalization of models in the statistical physics literature and is a natural finite analog for classes of graphexes. We describe a hypothesis testing algorithm that determines whether a graph came from a community configuration model or a traditional configuration model. This is joint work with Christian Borgs, Jennifer Chayes, Souvik Dhara, and Subhabrata Sen.

- Thursday, February 13, 2020, 4:15pm, at UNC, 125 Hanes Hall, Probability Seminar
*TBA*

Brendan Brown (UNC, Statistics and Operations Research) - Thursday, February 20, 2020, 4:15pm, at UNC, 125 Hanes Hall, Probability Seminar
*Epidemics on Evolving Graphs*

Dong Yao (Duke, math) - Thursday, February 27, 2020, 3:15pm, 119 Physics, Probability Seminar
*TBA*

Didong Li (Duke) - Thursday, March 19, 2020, 3:15pm, 119 Physics, Probability Seminar
*TBA*

Ted Cox (Syracuse, math) - Thursday, April 2, 2020, 3:15pm, 119 Physics, Probability Seminar
*TBA*

Avanti Athreya (Johns Hopkins) - Thursday, April 9, 2020, 3:15pm, 119 Physics, Probability Seminar
*TBA*

Allan Sly (Princeton, Mathematics) - Friday, April 10, 2020, 12:00pm, TBA, Colloquium Seminar
*TBA*

Allan Sly (Princeton University)

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