Title: Coalescing random walks and the Kingman coalescent model

Speaker: Johel Victorino Beltrán Ramírez (FGV EMAp e PUCP)

Our next seminar will be held on Monday, October 21, from 3:30 p.m. to 4:30 p.m. (Rio de Janeiro local time).  This meeting will take place at room C116 - Bloco C - CT – Instituto de Matemática – UFRJ. There will be no transmission online.

Abstract: Given a finite transitive graph and n particles labeled with numbers {1,2,3,...,n}, we place these particles on the set of vertices at random. Then, we let the particles evolve as a system of coalescing random walks: each particle performs a continuous-time simple random walk (SRW) and whenever two particles meet, they merge into one particle which continues to perform a SRW. At each time t, consider the partition P_t of {1,2,3,...,n} induced by the equivalence relation: i~j when particles i and j occupy the same vertex at time t. We show that the Kingman n-coalescent model emerges as a scaling limit for (P_t), as n is fixed and the size of the graph goes to infinity. This result allows me to talk about our main tool in our approach: the martingale problem.

Joint work with Enrique Chavez.

More complete information about the seminars can be found at

https://www.dme.ufrj.br/?page_id=3583

Sincerely,

Organizers: Giulio Iacobelli and Maria Eulalia Vares

More complete information about the seminars can be found at

https://www.dme.ufrj.br/?page_id=3583

Sincerely,

Organizers: Giulio Iacobelli and Maria Eulalia Vares