BEGIN:VCALENDAR
VERSION:2.0
PRODID:talks.ox.ac.uk
BEGIN:VEVENT
SUMMARY:Sub-diffusive scaling regimes for one-dimensional Mott variable-ra
nge hopping - David Croydon (RIMS\, Kyoto University)
DTSTART;VALUE=DATE-TIME:20230130T140000Z
DTEND;VALUE=DATE-TIME:20230130T150000Z
UID:https://talks.ox.ac.uk/talks/id/52a4341e-115a-48ee-88cf-4e32cc5f4a66/
DESCRIPTION:I will describe anomalous\, sub-diffusive scaling limits for a
one-dimensional version of the Mott random walk. The first setting consid
ered nonetheless results in polynomial space-time scaling. In this case\,
the limiting process can be viewed heuristically as a one-dimensional diff
usion with an absolutely continuous speed measure and a discontinuous scal
e function\, as given by a two-sided stable subordinator. Corresponding to
intervals of low conductance in the discrete model\, the discontinuities
in the scale function act as barriers off which the limiting process refle
cts for some time before crossing. I will outline how the proof relies on
a recently developed theory that relates the convergence of processes to t
hat of associated resistance metric measure spaces. The second setting con
sidered concerns a regime that exhibits even more severe blocking (and sub
-polynomial scaling). For this\, I will describe how\, for any fixed time\
, the appropriately-rescaled Mott random walk is situated between two\nenv
ironment-measurable barriers\, the locations of which are shown to have an
extremal scaling limit. Moreover\, I will give an asymptotic\ndescription
of the distribution of the Mott random walk between the barriers that con
tain it. This is joint work with Ryoki Fukushima (University of Tsukuba) a
nd Stefan Junk (Tohoku University).\nSpeakers:\nDavid Croydon (RIMS\, Kyot
o University)
LOCATION:Mathematical Institute (L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/52a4341e-115a-48ee-88cf-4e32cc5f4a66/
BEGIN:VALARM
ACTION:display
DESCRIPTION:Talk:Sub-diffusive scaling regimes for one-dimensional Mott va
riable-range hopping - David Croydon (RIMS\, Kyoto University)
TRIGGER:-PT1H
END:VALARM
END:VEVENT
END:VCALENDAR