Title

Linear Variance of First-Passage Percolation on the Book Graph

Date

2026年4月22日（水）　16:45-17:45
（16:15より数理研 2 階コモンルームでtea)　

Place

京都大学数理解析研究所 (RIMS) 110号室
(Rm110, Research Institute for Mathematical Sciences, Kyoto University)

Speaker

河本 野恵 (Noe Kawamoto)氏 （京大）

Abstract

　 We consider first-passage percolation (FPP) on the book graph with multiple pages, where upper-half planes are glued along the common axis. FPP was introduced by Hammersley and Welsh in 1965 as a model of fluid flow through a random medium. In the model, a non-negative random variable \( t_e \) is assigned on each edge of the graph, independently of the others. The passage time of a path is defined as the sum of the \( t_e \)'s over edges traversed by the path. Our interest is in the infimum of the passage times over all finite paths from \( o \) to \( ne_1 \), which is defined by \( T(0,ne_1) \). In this talk, we prove that when the number of pages of the book graph is sufficiently large, the variance of \( T(0,ne_1) \) is of order \( n \), which is markedly different from the conjectured behavior on two-dimentional integer lattice, where the variance is of order \( n^{2/3} \). This talk is based on joint work with Tzu-Han Chou (NUS) and Wai-Kit Lam (NTU).