OSU PROBABILITY SEMINARDepartment of Mathematics |
Day/Time/Room |
Speaker |
Title and abstract |
Tuesday, April 29, 4:00pm Kidder 350 |
Benjamin Young
University of Oregon |
"Inverting the Kasteleyn matrix for the Aztec Diamond" Abstract. I'll describe how to invert the Kasteleyn matrix for a few of the most interesting weight functions on the Aztec Diamond. This, in principle, allows the computations of correlation kernels for the associated tiling model. In some of the simpler cases, it is possible to compute asymptotics for this kernel rigorously; though this is essentially a combinatorics talk, I'll mention the sorts of asymptotics which can be derived. In more difficult cases (specifically 2-periodic weights) the asymptotics are not yet tractable, although they represent perhaps the most promising way in which one might study the transition between liquid and gaseous regimes in a dimer model. Joint work with Sunil Chhita and Kurt Johansson. |
Tuesday, May 6, 4:00pm Kidder 350 |
Zhen-Qing Chen
University of Washington |
"Anomalous diffusions and fractional order differential equations" Abstract. Anomalous diffusion phenomenon has been observed in many natural systems, from the signalling of biological cells, to the foraging behaviour of animals, to the travel times of contaminants in groundwater. I will first discuss the connections between anomalous diffusions and differential equations of fractional order, and then present some recent results in the study of heat kernels for non-local operators of fractional order. |
Tuesday, May 13, 4:00pm Kidder 350 |
Yung-Pin Chen
Lewis & Clark College |
"Making two integers coprime more likely" Abstract. I will introduce a Markov chain on the set of positive integers with the following transition probabilities: An integer will visit equally likely those integers that are coprime to it. I will discuss the probability of selecting two coprime integers if they are generated from the stationary distribution of this Markov chain. I will also discuss the evaluation of some series involving the Euler totient function. |
Tuesday, June 3, 4:00pm Kidder 350 |
Sooie-Hoe Loke
Oregon State University |
"On the Hitting Times of Integral of Geometric Brownian Motion" Abstract. The connection between Bessel process and the integral of geometric Brownian motion (IGBM) has been well-established. The key to this approach is the Lamperti relation. However, a common difficulty is that arguments constructed for Bessel processes with positive index generally do not carry over to the ones with negative index. In this talk, we use a differential equation approach to study the hitting times of IGBM. We discuss the paper by Metzler (2013) in which the Laplace transform of hitting times is expressed in terms of the gamma and confluent hypergeometric functions. The transform satisfies Kummer's equation which is obtained using Ito's formula and standard results on hitting times of diffusion processes. |