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SUMMARY:Flux Large Deviations - Robert Patterson (Weierstrass Institute\, 
 Berlin)
DTSTART:20190507T130000Z
DTEND:20190507T140000Z
UID:TALK123820@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:I will present an approach to proving a pathwise large deviati
 ons principle for pure jump interacting particle models of chemical reacti
 ons in the hydrodynamic limit.  I will show that working with the reaction
  fluxes as well as the reactant concentrations leads to an explicit rate f
 unction\, from which existing results can be recovered and even strengthen
 ed by applying the contraction principle.  The proof has two main technica
 l components—a stochastic tilting argument (change of measure) and an an
 alytic approximation argument.  These two steps are in a general sense sta
 ndard\, but their managing their interplay is key to avoiding awkward tech
 nical assumptions\, which we are able to do with the help of a continuity 
 assumption on the initial condition.\n\nIf the chemical reaction network c
 an be brought into detailed balance the large deviations rate function can
  be used to define a canonical gradient flow for the limiting system and t
 hus 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 coagul
 ating particles\, where the infinite number of possible sizes for an singl
 e particle makes the topological questions and analytic approximation argu
 ment more delicate.\n\nJoint work with Michiel Renger
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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