Pure Maths Colloquium: Discrete heat kernels and counting in Cayley graphs
24 January 2011 17:15 in CM221
We find that heat kernels of finitely generated groups are built up from terms whose main factors are Bessel functions. These explicit expressions allow for analyses of counting functions, such as the number of spanning trees or closed geodesics. Interesting constants appear in the asymptotics of counting functions in certain families of graphs: L^2 determinants, Mahler measures, determinants of Laplacians, zeta functions, automorphic forms, etc. Joint work with G. Chinta and J. Jorgenson.
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