# Probability Seminar

The probability seminar is coordinated with Duke University. For more talks check the calendar at Duke.

## April 2016

### Probability Seminar: Harry Crane, Rutgers University

Probabilistic symmetries in networks I discuss various refinements and extensions of the principle of exchangeability, focusing on 3 specific cases: 1. Relative exchangeability, by which the distribution of a random graph is invariant with respect to the symmetries of some other structure. 2. Combinatorial Markov processes for temporally varying networks. 3. Edge exchangeable random graphs, a new invariance principle that resolves a major challenge in modeling network datasets that are sparse and/or exhibit power law degree distributions. Each case leads…

Find out more »## September 2016

### Probability Seminar: Haya Kaspi, Technion-Israel Institute of Technology

An Infinite-Dimensional Skorohod Map and Continuous Parameter Priorities (Joint work with Rami Atar, Anup Biswas and Kavita Ramanan) The Skorokhod map on the half-line has proved to be a useful tool for studying processes with non-negativity constraints. In this lecture I will introduce a measure-valued analog of this map that transforms each element of a certain class of càdlàg paths that take values in the space of signed measures on the positive half line to a càdlàg path that takes…

Find out more »## November 2016

### Probability Seminar: Jay Newby, UNC-CH

Probability Seminar Thursday, November 3, 2016 Hanes 125 4:15 PM Jay Newby University of North Carolina-Chapel Hill An artificial neural network approach to automated particle tracking analysis of 2D and 3D microscopy videos Tracking of microscopic species is one of the most utilized experimental technologies in materials science, biophysics, tissue engineering and nanomedicine. The goal is to draw inferences (e.g., viscous and elastic moduli, mesh spacings, passage times) by statistical analysis of particle traces. This in turn allows for…

Find out more »## December 2016

### Probability Seminar: Dieter Mitsche, Universite de Nice Sophia-Antipolis

“On the spectral gap of random hyperbolic graphs” Random hyperbolic graphs have been suggested as a promising model of social networks. A few of their fundamental parameters have been studied. However, none of them concerns their spectra. We consider the random hyperbolic graph model as formalized by Gugelmann et al. and essentially determine the spectral gap of their normalized Laplacian. Specifically, we establish that with high probability the second smallest eigenvalue of the normalized Laplacian of the giant component…

Find out more »## January 2017

### Probability Seminar: Michael Perlmutter, UNC-CH

Michael Perlmutter UNC-Chapel Hill Department of Statistics and Operations Research Martingale Transforms and their Applications to Harmonic Analysis Martingale transform methods are a powerful tool for the study of many operators of classical interest in harmonic analysis such as the Riesz transforms and the Beurling-Ahlfors transform. In particular, these methods allow us to transfer D.L. Burkholder’s sharp constant, p*-1, for the boundedness of martingale transforms to a large class of analytic operators. I will discuss the history of such…

Find out more »## April 2017

### Probability Seminar: Wilfrid Kendall, University of Warwick

Wilfrid Kendall University of Warwick A Dirichlet Form approach to MCMC Optimal Scaling (Joint with Giacomo Zanella and Mylene Bédard) In this talk I will discuss the use of Dirichlet forms to deliver proofs of optimal scaling results for Markov chain Monte Carlo algorithms (specifically, Metropolis-Hastings random walk samplers) under regularity conditions which are substantially weaker than those required by the original approach (based on the use of infinitesimal generators). The Dirichlet form method has the added advantage of…

Find out more »## October 2017

### Probability Seminar: Natalie Stanley, UNC-CH

Compressing Networks with Super Nodes Community detection is a commonly used technique for identifying cohesive groups of nodes in a network, based on similarities in connectivity patterns. To facilitate community detection in large networks, we recast the original network as a smaller network of 'super nodes', where each super node is comprised of one of more nodes of the original network. We can then use this super node representation as the input into standard community detection algorithms. To define the…

Find out more »## November 2017

### Probability Seminar: Suman Chakraborty

Suman Chakraborty University of North Carolina-Chapel Hill Pseudo-random graphs and applications We consider classes of pseudo-random graphs on n vertices for which the degree of every vertex and the co-degree between every pair of vertices are in the intervals (np-Cn^δ,np+Cn^δ) and (np^2-Cn^δ,np^2+Cn^δ) respectively, for some absolute constant C, and p,δ∈(0,1). We show that for such pseudo-random graphs the number of induced isomorphic copies of subgraphs of size s are approximately same as that of an Erdos-Renyi random graph with edge…

Find out more »### Probability Seminar: Eric Friedlander

Mean-Field Methods in Large Stochastic Networks Analysis of large-scale communication networks (e.g. ad hoc wireless networks, cloud computing systems, server networks etc.) is of great practical interest. The massive size of such networks frequently makes direct analysis intractable. Asymptotic approximations using hydrodynamic and diffusion scaling limits provide useful methods for approaching such problems. In this talk, we study two examples of such an analysis. In the first, we present an asymptotic method of solving control problems in such networks. In…

Find out more »## April 2018

### Probability Seminar: James Nolan, Duke University

Probability Seminar Thursday, April 5, 2018 Hanes 125 4:15 PM James Nolan Mathematics Department Duke University A system of Brownian particles interacting through a moving reflector I will describe a system of N particles diffusing on the real line and interacting through a moving boundary. The hydrodymamic limit (N going to infinity) of this system is a solution to a nonlinear free-boundary problem for the heat equation. For finite N, the stochastic system has a stationary distribution, a fact that…

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