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CATEGORIES:Probability
SUMMARY:Flux Large Deviations - Robert Patterson (Weierstr
ass Institute\, Berlin)
DTSTART;TZID=Europe/London:20190507T140000
DTEND;TZID=Europe/London:20190507T150000
UID:TALK123820AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/123820
DESCRIPTION:I will present an approach to proving a pathwise l
arge deviations principle for pure jump interactin
g particle models of chemical reactions in the hyd
rodynamic limit. I will show that working with th
e reaction fluxes as well as the reactant concentr
ations leads to an explicit rate function\, from w
hich existing results can be recovered and even st
rengthened by applying the contraction principle.
The proof has two main technical componentsâ€”a sto
chastic tilting argument (change of measure) and a
n analytic approximation argument. These two step
s are in a general sense standard\, but their mana
ging their interplay is key to avoiding awkward te
chnical assumptions\, which we are able to do with
the help of a continuity assumption on the initia
l condition.\n\nIf the chemical reaction network c
an be brought into detailed balance the large devi
ations rate function can be used to define a canon
ical gradient flow for the limiting system and thu
s give a rigorous derivation of the thermodynamic
free energy. However\, the proof does not require
any form of reversibility and so I will make some
comments about ongoing work to extend the result
to systems of coagulating particles\, where the in
finite number of possible sizes for an single part
icle makes the topological questions and analytic
approximation argument more delicate.\n\nJoint wor
k with Michiel Renger
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Perla Sousi
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