Department of Mathematics

 Fall 2014

We will meet on Tuesdays at 4:00pm.
Here is a tentative list of speakers (to be extended): Debashis Mondal (Department of Statistics), Anatoly Yambartsev (University of São Paulo, Brazil), Yevgeniy Kovchegov
Registration information: Mth 607, Sec 005 - CRN 13894



Title and abstract

Tuesday, October 21, 4:00pm
Kidder 238
Anatoly Yambartsev
University of São Paulo, Brazil

"Large deviations for excursions of M/M/∞"

Abstract. We derive a large deviations principle for the trajectories generated by a class of ergodic Markov processes. Specifically, we work with M/M/∞ queueing processes. We study large deviations of these processes scaled equally in both space and time directions. Our main result is that the probabilities of long excursions originating at state 0 would converge to zero function with the rate proportional to the square of the scaling parameter. The rate function is expressed as an integral of a linear combination of trajectories.
Tuesday, November 11, 4:00pm
Kidder 238
Debashis Mondal
Department of Statistics, Oregon State University

"Applying Dynkin's isomorphism: an alternative approach to understand the Markov property of the de Wijs process"

Abstract. Dynkin's (1980) seminal work associates a multidimensional Markov process with a multidimensional Gaussian random field. This association, known as Dynkin's isomorphism, has profoundly influenced the studies of Markov properties of generalized Gaussian random fields. In this talk, applying Dykin's isomorphism, we shall investigate a particular generalized Gaussian Markov random field, namely, the de Wijs process that originated in Georges Matheron's pioneering work on mining geostatistics and, following McCullagh (2002), is now receiving renewed attention in spatial statistics. Dynkin's theory grants us further insight into Matheron's kriging formula for the de Wijs process and highlight previously unexplored relationships of the central Markov models in spatial statistics with random walks and the Brownian motion on the plane.
Tuesday, November 25, 4:10pm
Kidder 356
Anatoly Yambartsev
University of São Paulo, Brazil

"Phase transition in ferromagnetic Ising model with a cell-board external field"

Abstract. We show the presence of a first-order phase transition for a ferromagnetic Ising model on integer 2 dimensional lattice with a periodical external magnetic field. The external field takes two values h and -h, where h>0. The sites associated with positive and negative values of external field form a chessboard configuration with rectangular cells of sides L_1xL_2 sites. The phase transition holds if h is small enough. We prove a first-order phase transition using reflection positivity (RP) method. We apply a key inequality which is usually referred to as the chessboard estimate. This is a joint work with E. Pechersky and M. Gonzalez, my PhD student.

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,