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SUMMARY:Expander graphs are globally synchronising - Victor Souza\, Cambri
 dge
DTSTART:20221121T160000Z
DTEND:20221121T170000Z
UID:TALK193094@talks.cam.ac.uk
CONTACT:Roland Bauerschmidt
DESCRIPTION:The Kuramoto model is a prototypical model used for rigorous m
 athematical analysis in the field of synchronisation and nonlinear dynamic
 s. A realisation of this model consists of a collection of identical oscil
 lators with interactions given by a network\, which we identify respective
 ly with vertices and edges of a graph. We show that a graph with sufficien
 t expansion must be globally \n synchronising\, meaning that the Kuramoto 
 model on such a graph will converge to the fully synchronised state with a
 ll the oscillators with same phase\, for every initial state up to a set o
 f measure zero. In particular\, we show that for p ≥ (1 + eps)(log n)/n\
 , the Kuramoto \n model on the Erdős--Rényi graph G(n\,p) is globally sy
 nchronising with high probability\, settling a conjecture of Ling\, Xu and
  Bandeira. We also show the global synchrony of any d-regular Ramanujan gr
 aph with d ≥ 600.\n\nJoint work with P. Abdalla\, A. Bandeira\, M. Kassa
 bov\, S. Strogatz and A. Townsend.
LOCATION:MR14\, Centre for Mathematical Sciences
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