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SUMMARY:A probabilistic approach to Carne's bound - Remi Peyre (UPMA
DTSTART:20110215T163000Z
DTEND:20110215T173000Z
UID:TALK28863@talks.cam.ac.uk
CONTACT:Berestycki
DESCRIPTION:In this talk I will speak about a 1985 result from Carne & Var
 opoulos: consider a Markov chain on a graph (i.e. whose transitions always
  follow the edges) which is reversible with stationary measure $\\mu$\; th
 en\, denoting by $p^t(x\,y)$ the probability that a chain starting at $x$ 
 is at $y$ at time $t$\, one has the Gaussian bound \\[ p^t(x\,y) \\leq \\s
 qrt{e} \\big( \\mu(y)/\\mu(x) \\big)^{1/2} \\exp \\big( -d(x\,y)^2 / 2t \\
 big) \,\\] where $d(x\,y)$ is the graph distance between $x$ and $y$. My g
 oal will be to explain this result by probabilistic arguments (which was n
 ot the case of the original proof)\, close to the forward/ backward martin
 gale decomposition. This approach will lead to a generalization of Carne's
  bound to the case where the particle can occasionally make a jump not fol
 lowing an edge. I will also explain how one can improve Carne's bound by a
  spectral factor\, by considering the chain "conditioned to be recurrent".
  
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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