Seminar Details
Minimal Cuts in the Z^D Lattice with Random Capacities
- Start Date: January 29, 2024
- Event Start Time: 2:00 PM
- Event End Time: 3:00 PM
- Seminar Series: Rutgers Discrete Mathematics Seminar
- Presenter(s): Ron Peled - Tel-Aviv University
- Event Location: Hill Center, Room 005
- Event Additional Info: <p>See: <a href="https://sites.google.com/view/rutgersdmseminar" id="OWA95d0fea6-0265-ed2f-6395-3caa2051c033" rel="noopener noreferrer" target="_blank" title="https://sites.google.com/view/rutgersdmseminar">https://sites.google.com/view/rutgersdmseminar</a></p>
- Presentation Type: Stand Alone Presentation
- Abstract:
Endow the edges of the Z^D lattice with independent and identically distributed random capacities (e.g., uniformly distributed on [a,b] for some b>a>0). We wish to study the minimal cuts in the resulting network. Our focus is on the following setup: Consider the cube {-L,..., L}^D and the minimal cut separating the "upper" and "lower" halves of the boundary of the cube. How flat is this cut?
It is believed that the minimal cut is (power-law) rough in dimensions D=2,3 and flat in dimensions D>=6, and that it undergoes a roughening phase transition in dimension D=4 as the capacity distribution becomes more spread out. The case of dimension D=5 is more subtle. We discuss these predictions as well as rigorous results, and further mention rigorous results on related models of minimal surfaces in random environment.
The above combinatorial problem is further motivated by relations with first-passage percolation and disordered statistical physics models.
Based on joint works with Michal Bassan and Shoni Gilboa and with Barbara Dembin, Dor Elboim and Daniel Hadas.