Bernard Derrida – Collège de France and ENS Paris
Wednesday, March 26th , 10:45AM DST
Overlaps in spin glasses and models of evolution
Overlaps play a central role in the theory of spin glasses. In the mean field case their fluctuations obey simple universal laws, which are related to sums of i.i.d. random variables with heavy tails. These laws can alternatively be derived by combinatorial methods using the replica approach.
In models of evolution, the genetic distance between individuals plays the role of the overlaps in spin glasses. The statistics of these genetic distances are qualitatively similar to those of overlaps in spins glasses in the case of neutral asexual evolution (the Kingman coalescent) and become identical to those of spin glasses in presence of selection (N-Branching Brownian motion).