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SUMMARY:Determinants of Laplacians of converging surfaces - Renan Gross (T
 el Aviv)
DTSTART:20231024T130000Z
DTEND:20231024T140000Z
UID:TALK207664@talks.cam.ac.uk
CONTACT:Jason Miller
DESCRIPTION:The "tree entropy" of a converging sequence of graphs roughly 
 counts how many spanning trees per vertex each graph has\, and can be calc
 ulated using the Laplacian of the graph.\n\nIn this talk\, we will discuss
  a similar quantity for compact hyperbolic surfaces. We show that\, under 
 some assumptions on the eigenvalues and short geodesics\, if a sequence of
  surfaces converges to a random rooted surface\, then the logarithm of the
  determinant of its Laplacian converges to a constant. The proof involves 
 analyzing the return density of Brownian motion to the origin\, averaged o
 ver the entire surface.
LOCATION:MR12
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