OSU PROBABILITY SEMINARDepartment of Mathematics |
Day/Time/Room |
Speaker |
Title and abstract |
Tuesday, April 5, 3:30 pm GILK 115 |
Jayadev S. Athreya
University of Washington |
"The Erdos-Szusz-Turan distribution" Abstract. Dirichlet's theorem on diophantine approximation states that for any irrational number a, there are infinitely many rationals p/q so that q|aq-p| < 1. Erdos-Szusz-Turan asked the question of the probability that this estimate could be improved to q|aq-p|< A, with q in a fixed range [N, cN], and the behavior of this probability as N grows. We answer their question and provide a wide-ranging generalization to the setting of equivariant point processes. This is joint work with Anish Ghosh. |
Tuesday, May 3, 4:00 pm GILK 115 |
Yevgeniy Kovchegov
Oregon State University |
"Horton-Strahler ordering and Tokunaga indexing in stochastic processes" Abstract. We introduce a class of stochastic processes that we call hierarchical branching processes. By construction, the processes satisfy the Tokunaga, and hence Horton, self-similarity constraints. Taking the limit of averaged stochastic dynamics, we obtain the deterministic system of differential equations that describe the temporal dynamics of a Tokunaga branching system. In particular, we study the averaged tree width function to establish a phase transition in the Tokunaga dynamics that separates fading and explosive branching. We then describe a class of critical hierarchical branching processes (that happen at the phase transition boundary) that includes as a special case the celebrated critical Galton-Watson branching process. We illustrate efficiency of the critical hierarchical branching processes in describing diverse observed dendritic structures, and discuss the related critical phenomena from the point of view of respective applications. Joint work with Ilya Zaliapin (University of Nevada Reno). |
Tuesday, May 17, 4:00 pm GILK 115 |
Andrey Sarantsev
Department of Statistics and Applied Probability University of California, Santa Barbara. |
TBA Abstract. TBA |
Tuesday, May 24, 4:00 pm GILK 115 |
Amber Puha
California State University, San Marcos |
TBA Abstract. TBA |