[Turkmath:4463] Analiz Semineri

[H. Turgay Kaptanoglu]

Degerli Liste Uyeleri,

Bilkent Universitesi Matematik Bolumu Analiz Seminerinin bir sonraki
konusmasi asagidaki gibidir.

Erik Bates (University of California, Berkeley)

Empirical measures, geodesic lengths, and a variational formula in 
first-passage percolation.

We consider the standard first-passage percolation model on Z^d, in 
which each edge is assigned an i.i.d. non-negative weight, and the 
passage time between any two points is the smallest total weight of a 
nearest-neighbor path between them.  Our primary interest is in the 
empirical measures of edge-weights observed along geodesics from 0 to 
ne_1.  For various dense families of edge-weight distributions, we prove 
that these measures converge weakly to a deterministic limit as n tends 
to infinity.  These families include arbitrarily small 
L^infty-perturbations of any given distribution, as well as almost every 
finitely supported distribution.  Analogous results hold for 
e_1-directed infinite geodesics.  Our methodology is driven by a new 
variational formula for the time constant, which requires no assumptions 
on the edge-weight distribution.  Incidentally, this variational 
approach allows us to recover and extend a recent result of Krishnan, 
Rassoul-Agha, and Seppäläinen regarding the convergence of geodesic 
lengths.

12 Mayis 2020 Sali, 16:00-17:00.

Konusma dili Ingilizcedir.

Katilmak isteyenlerin zoom sifresi almak icin 11 Mayis Pazartesi gunune 
kadar
goncha at fen.bilkent.edu.tr  adresinde seminer koordinatoru Alexander
Goncharov'a bir e-mail gondermeleri rica olunur.

Saygilarimizla,

HTK