TY - JOUR
T1 - Random methods in 3-manifold theory
AU - Lubotzky, Alexander
AU - Maher, Joseph
AU - Wu, Conan
N1 - Publisher Copyright:
© 2016, Pleiades Publishing, Ltd.
PY - 2016
Y1 - 2016
N2 - The surface map arising from a random walk on the mapping class group may be used as the gluing map for a Heegaard splitting, and the resulting 3-manifold is known as a random Heegaard splitting. We show that the splitting distance of random Heegaard splittings grows linearly in the length of the random walk, with an exponential decay estimate for the proportion with slower growth. We use this to obtain the limiting distribution of Casson invariants of random Heegaard splittings.
AB - The surface map arising from a random walk on the mapping class group may be used as the gluing map for a Heegaard splitting, and the resulting 3-manifold is known as a random Heegaard splitting. We show that the splitting distance of random Heegaard splittings grows linearly in the length of the random walk, with an exponential decay estimate for the proportion with slower growth. We use this to obtain the limiting distribution of Casson invariants of random Heegaard splittings.
UR - http://www.scopus.com/inward/record.url?scp=84971324306&partnerID=8YFLogxK
U2 - 10.1134/S0081543816010089
DO - 10.1134/S0081543816010089
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AN - SCOPUS:84971324306
SN - 0081-5438
VL - 292
SP - 118
EP - 142
JO - Proceedings of the Steklov Institute of Mathematics
JF - Proceedings of the Steklov Institute of Mathematics
IS - 1
ER -