![[Search]](/static/images/search.gif){kind=small}
![[A-Z Index]](/static/images/az.gif){kind=small}
![[Contact]](/static/images/contact.gif){kind=small}
![[University of Cambridge]](/static/images/identifier2.gif){kind=small}
![[Talks.cam]](/static/images/talkslogosmall.gif)
Erik Bates, University of Wisconsin-Madison 
Tuesday 02 November 2021, 14:00-15:00
Empirical measures, geodesic lengths, and a variational formula in first-passage percolation
- 👤 Speaker: Erik Bates, University of Wisconsin-Madison
- 📅 Date & Time: Tuesday 02 November 2021, 14:00 - 15:00
- 📍 Venue: MR12 Centre for Mathematical Sciences
Abstract
We consider the standard first-passage percolation model on Z^d, in which each edge is assigned an i.i.d. nonnegative weight, and the passage time between any two points is the smallest total weight of a nearest-neighbor path between them. This induces a random ``disordered” geometry on the lattice. Our primary interest is in the empirical measures of edge-weights observed along geodesics in this geometry, say from 0 to [n\xi], where \xi is a fixed unit vector. For various dense families of edge-weight distributions, we prove that these measures converge weakly to a deterministic limit as n tends to infinity. The key tool is a new variational formula for the time constant. In this talk, I will derive this formula and discuss its implications for the convergence of both empirical measures and lengths of geodesics.
Series This talk is part of the Probability series.
Included in Lists
- All CMS events
- All Talks (aka the CURE list)
- bld31
- CMS Events
- DPMMS info aggregator
- DPMMS lists
- DPMMS Lists
- Hanchen DaDaDash
- Interested Talks
- MR12 Centre for Mathematical Sciences
- Probability
- School of Physical Sciences
- Statistical Laboratory info aggregator
Note: Ex-directory lists are not shown.