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SUMMARY:Linard Hoessly (University of Copenhagen)
DTSTART:20210325T160000Z
DTEND:20210325T163000Z
DTSTAMP:20260421T125614Z
UID:MoRN/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MoRN/15/">On
  an algebraic approach to product-form stationary distributions of some re
 action networks</a>\nby Linard Hoessly (University of Copenhagen) as part 
 of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nExact re
 sults for product-form stationary distributions of Markov chains are of in
 terest in different fields. In stochastic reaction networks (CRNs)\, stati
 onary distributions are mostly known in special cases where they are of pr
 oduct-form. However\, there is no full characterization of the classes of 
 networks whose stationary distributions have product-form. We develop an a
 lgebraic approach to product-form stationary distributions in the framewor
 k of CRNs. Under certain hypotheses on linearity and decomposition of the 
 state space for conservative ergodic CRNs\, this gives sufficient and nece
 ssary algebraic conditions for product-form stationary distributions. Corr
 espondingly we obtain a semialgebraic subset of the parameter space that c
 aptures rates where\, under the corresponding hypotheses\, CRNs have produ
 ct-form. We employ the developed theory to CRNs and some models of statist
 ical mechanics\, besides sketching the pertinence in other models from app
 lied probability.\n
LOCATION:https://researchseminars.org/talk/MoRN/15/
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