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BEGIN:VEVENT
DTSTAMP:20260507T141704Z
DTSTART:20260520T140000Z
DTEND:20260520T150000Z
SUMMARY:Probability Seminar: Edward Crane - Coupling Markov chains with a
  common image chain
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}h26e-movklb
 hw-1a6w1m
DESCRIPTION:Edward Crane (University of Bristol) will speak at the Probab
 ility seminar.\n\nTitle:  Coupling Markov chains with a common image cha
 in\n\nAbstract: (Joint work with Erin Russell and Alexander Holroyd\, mo
 stly in arXiv:2604.12853)\n \nYou are given two homogeneous Markov chain
 s X and Y with countable state spaces A and B and specified initial dist
 ributions\, and you are given a subset U of A x B. How can you decide wh
 ether there exists a homogeneous Markov chain taking values in U that is
  a coupling of X and Y? \n\n An interesting special case is when U is a 
 `block diagonal' set of the form {(a\,b): f(a) = g(b)}\, for maps f and 
 g from A and B to a third state space C.  We construct a Markov chain co
 upling taking values in this set in the case where the image processes f
 (X) and g(Y) are equal in law to a homogeneous Markov chain on C. (In hi
 ghbrow language this shows that the Ore property holds for the category 
 of countable homogeneous Markov chains with weak lumpings as morphisms.)
  \n\nI will present a simple example which shows that for the Markov cha
 in coupling to exist it is not sufficient for f(X) and g(Y) to have the 
 same law as processes if the common image process is not required to be 
 a homogeneous Markov chain.\n\nI will also explain our original motivati
 on for this problem\, which came from comparing a directed graph  versio
 n of the Ráth-Tóth mean field forest fire model with the original undire
 cted graph model.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 2\, Alan Turing Building\, Manchester
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