Join us for these events hosted by the Department of Mathematics, including colloquia, seminars, graduate student defenses and outreach, or of interest to Mathematicians hosted by other groups on campus.
Cross-Multiplicative Coalescent Processes and Applications
STAG 112
Graduate Student SeminarSpeaker: Aren Lampman
The talk is based on the paper by Y. Kovchegov, P. T. Otto, and A. Yambartsev (ALEA, Lat. Am. J. Probab. Math. Stat. 18, 81–106 (2021)).Here is the original abstract:We introduce and analyze a novel type of coalescent processes called cross-multiplicative coalescent that models a system with two types of particles, A and B. The bonds are formed only between the pairs of particles of opposite types with the same rate for each bond, producing connected components made of particles of both types. We analyze and solve the Smoluchowski coagulation system of equations obtained as a hydrodynamic limit of the corresponding Marcus- Lushnikov process. We establish that the cross-multiplicative kernel is a gelling kernel, and find the gelation time. As an application, we derive the limiting mean length of a minimal spanning tree on a complete asymmetric bipartite graph with independent edge weights, distributed uniformly over [0, 1]. Read more.