Department of Mathematics

 Spring 2017

We will meet on Tuesdays at 4:00 pm.
Here is a tentative list of speakers (to be extended): Mathew Titus, Yevgeniy Kovchegov, Sharmodeep Bhattacharyya
Registration information: Mth 607, Sec 003 - CRN 54007



Title and abstract

Tuesday, April 18, 4:00 pm
GILK 100
Yevgeniy Kovchegov
Oregon State University

"Coalescence and minimal spanning trees of irregular graphs"

Abstract. We devise a method of finding the limiting mean length of a minimal spanning tree for a random graph via the Smoluchowski coagulation equations for the corresponding coalescent process. In particular, we use this approach for finding the limiting mean length of a minimal spanning tree for the Erdos-Renyi random graph on an asymmetric bipartite graph, producing a completely new formula yet consistent with the previously known formula for the symmetric bipartite graph.

Joint work with Peter T. Otto of Willamette University and Anatoly Yambartsev of University of São Paulo.
Tuesday, May 9, 4:00 pm
GILK 100
Sharmodeep Bhattacharyya
Statistics Department
Oregon State University

"Spectral Clustering for Dynamic Block Models"

Abstract. One of the most common and crucial aspects of many network data sets is the dependence of network link structure on time. In this work, we consider the problem of finding a common clustering structure in time-varying networks. We also propose an extension of the static version of nonparametric latent variable models into the dynamic setting and use special cases of the dynamic models to justify the spectral clustering methods. We consider two extensions of spectral clustering methods to dynamic settings and give theoretical guarantee that the spectral clustering methods produce consistent community detection in case of both dynamic stochastic block model and dynamic degree-corrected block model. The methods are shown to work under sufficiently mild conditions on the number of time snapshots of networks and also if the networks at each time snapshot are sparse and networks at most time snapshots are below community detectability threshold. We show the validity of the theoretical results via simulations too. (Joint work with Shirshendu Chatterjee, CUNY)
Tuesday, May 30, 4:00 pm
GILK 100
Mathew Titus
Oregon State University

"Mixing times for diffusive systems"

Abstract. Mixing times measure how quickly a Markov process approaches its stationary distribution. Often computer scientists and statistical physicists use Markov chains to model networks with n nodes or physical systems with n particles and are interested in the mixing time as a function of large n. In this talk we explore a novel and general method of computing the mixing time asymptotics for one-dimensional diffusive Markov chains. The related question of which chains exhibit cutoff phenomena and with what window-size is also discussed.

Past probability seminars: Fall 2005, Winter 2006, Spring 2006, Fall 2006, Winter 2007, Spring 2007, Fall 2007, Winter 2008, Spring 2008, Fall 2008, Winter 2009, Spring 2009, Fall 2009, Winter 2010, Spring 2010, Fall 2010, Winter 2011, Spring 2011, Fall 2011, Winter 2012, Spring 2012, Fall 2012, Winter 2013, Spring 2013, Fall 2013, Winter 2014, Spring 2014, Fall 2014, Winter 2015, Spring 2015, Fall 2015, Winter 2016, Spring 2016, Fall 2016, Winter 2017