Asymptotic behavior of first passage time in the frog model.
Báo cáo viên: Cấn Văn Hảo

Thời gian: 14h, Thứ 5, ngày 19 tháng 12 năm 2019

Địa điểm: Phòng 611-612, Nhà A6, Viện Toán học

Tóm tắt: Frog models are simple but well-known models in the study of the spread of infection. In these models, individuals (also called frogs) move on the integer lattice $Z^d$, which have one of two states infected (active) and healthy (passive). We assume that at the beginning, there is only one infected frog at the origin, and there are healthy frogs at other sites of $Z^d$. When a healthy frog encounters with an infected one, it becomes infected forever. While the healthy frogs do not move, the infected frogs  perform independent simple random walks. In this talk, we will discuss on the asymptotic behavior, in particular a law of large numbers, fluctuation, large deviation estimates, of the time a given vertex gets infection.

Based on joint work with Naoki Kubota and Shuta Nakajima

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