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DTSTART;TZID=America/Toronto:20260210T093000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20260210T103000
URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-162
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:NIKITA LVOV\n\n_Random Walks arising in Random Matrix Theory_\n
 \nThe cokernel of a large p-adic random matrix M is a random abelian\np-gr
 oup. Friedman and Washington showed that its distribution\nasymptotically 
 tends to the well-known Cohen-Lenstra distribution. We\nstudy an irreducib
 le Markov chain on the category of finite abelian\np-groups\, whose statio
 nary measure is the Cohen-Lenstra distribution.\nThis Markov chain arises 
 when one studies the cokernels of corners of\nM. We show two surprising fa
 cts about this Markov chain. Firstly\, it\nis reversible. Hence\, one may 
 regard it as a random walk on finite\nabelian p-groups. The proof of rever
 sibility also explains the\nappearance of the Cohen-Lenstra distribution i
 n the context of random\nmatrices. Secondly\, we can explicitly determine 
 the spectrum of the\ninfinite transition matrix associated to this Markov 
 chain. Finally\,\nwe show how these results generalize to random matrices 
 over general\npro-finite local rings.\n\nMC 5403
DTSTAMP:20260407T211617Z
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