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Abhijit Champanerkar and Ilya Kofman
Determinant density and biperiodic alternating links view print
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| Published: |
August 23, 2016 |
| Keywords: |
Spanning tree entropy, Mahler measure, knot determinant, dimer model, Følner convergence |
| Subject: |
Primary: 57M25, 05A16; secondary: 57M50, 05C30 |
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Abstract
Let L be any infinite biperiodic alternating link. We show that
for any sequence of finite links that Følner converges almost
everywhere to L, their determinant densities converge to the Mahler
measure of the 2-variable characteristic polynomial of the toroidal
dimer model on an associated biperiodic graph.
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| Acknowledgements
The authors acknowledge support by the Simons Foundation and PSC-CUNY. The first author also thanks the Columbia University Mathematics Department for its hospitality during his sabbatical leave.
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| Author information
Abhijit Champanerkar:
Department of Mathematics, College of Staten Island & The Graduate Center, City University of New York, New York, NY
abhijit@math.csi.cuny.edu
Ilya Kofman:
Department of Mathematics, College of Staten Island & The Graduate Center, City University of New York, New York, NY
ikofman@math.csi.cuny.edu
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