OSU PROBABILITY SEMINARDepartment of Mathematics |
Day/Time/Room |
Speaker |
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. |