Tid: 24 november 2008 kl 15.15 .

Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!

Föredragshållare: Michael Björklund, Matematik, KTH, Foto

Titel: First passage percolation and random matrix products.

Sammanfattning: First passage percolation on Z^d is a natural extension of the subadditive ergodic theory developed by Hammersley and Kingman in the late 1960's. It can roughly be described as the geometry of random semimetric spaces; and most of the classical theorems concern the large scale behaviour of such spaces. One of the main results in this theory is the asymptotic shape theorem (usually attributed to Cox-Durrett in the i.i.d. situation), which asserts that the shape of large balls in an (inner) random semimetric behaves non-randomly on a certain scale. In one dimension, this reduces to the classical ergodic theorem by Birkhoff. In this talk I will describe a general, non-linear, generalization of the asymptotic shape theorem. The developed techniques also yield interesting results when reduced to one dimension. Examples include the multiplicative ergodic theorem by Osceledec.

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