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SUMMARY:Geometrical Optics of Constrained Brownian Motion
DTSTART;VALUE=DATE-TIME:20201204T085000Z
DTEND;VALUE=DATE-TIME:20201204T091000Z
DTSTAMP;VALUE=DATE-TIME:20220810T000133Z
UID:indico-contribution-398@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Baruch Meerson (Hebrew University of Jerusalem)\nThe
optimal fluctuation method — essentially geometrical optics — gives a
valuable insight into large deviations of constrained Brownian motion\, a
nd it achieves this purpose by simple means. I will illustrate these poin
ts by revisiting the Airy distribution - the probability distribution of t
he \narea under a Brownian excursion - and considering some additional sta
tistics of Brownian excursions. \n\nThe geometrical optics immediately giv
es the large-area tail of the Airy distribution. It also predicts the posi
tion distribution of a Brownian excursion at an intermediate time\, condit
ioned on a large area. Finally\, it gives the area distribution on a sub-
interval of Brownian excursion. The last two distributions exhibit dynamic
al phase transitions which have a simple geometric origin.\n\nhttps://zako
pane.if.uj.edu.pl/event/16/contributions/398/
LOCATION:
URL:https://zakopane.if.uj.edu.pl/event/16/contributions/398/
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