BEGIN:VCALENDAR
VERSION:2.0
PRODID:talks.ox.ac.uk
BEGIN:VEVENT
SUMMARY:The critical window for random transposition random walk
- Dominic Yeo (University of Oxford)
DTSTART;VALUE=DATE-TIME:20190513T110000Z
DTEND;VALUE=DATE-TIME:20190513T120000Z
UID:https://talks.ox.ac.uk/talks/id/6b578653-67d5-464d-862b-cc51f568404d/
DESCRIPTION:The random walk on the permutations of [N] generated by the tr
anspositions was shown by Diaconis and Shahshahani to mix with sharp cutof
f around N log N /2 steps. However\, Schramm showed that the distribution
of the sizes of the largest cycles concentrates (after rescaling) on the P
oisson-Dirichlet distribution PD(0\,1) considerably earlier\, after (1+\\e
psilon)N/2 steps. We show that this behaviour in fact emerges precisely du
ring the critical window of (1+\\lambda N^{-1/3}) N/2 steps\, as \\lambda
\\rightarrow\\infty. Our methods are rather different\, and involve an an
alogy with the classical Erdos-Renyi random graph process\, the metric sca
ling limits of a uniformly-chosen connected graph with a fixed finite numb
er of surplus edges\, and analysing the directed cycle structure of large
3-regular graphs. Joint work with Christina Goldschmidt.\nSpeakers:\nDomin
ic Yeo (University of Oxford)
LOCATION:Mathematical Institute\, Woodstock Road OX2 6GG
URL:https://talks.ox.ac.uk/talks/id/6b578653-67d5-464d-862b-cc51f568404d/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:The critical window for random transposition random walk
- Dominic Yeo (University of Oxford)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
END:VCALENDAR