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SUMMARY:How to replace random walk representations in models that don't ha
 ve one? - Erwin Bolthausen (Zurich)
DTSTART:20170524T151500Z
DTEND:20170524T161500Z
UID:TALK72417@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:Random walk representations for the correlations of random fie
 lds have played a considerable role in the past. For instance\, the correl
 ations of gradient models have such a representation if the interactions a
 re given by a convex function of the gradient. Also\, correlations for gra
 dient models with local pinning have been analyzed in great details using 
 random walks with traps\, see e.g. [1]\, where very detailed properties of
  the range of a random walk played a crucial role. In recent years\, there
  had been interest in random fields which don't admit a direct random walk
  representation\, for instance so-called membrane models. In a recent pape
 r with Alessandra Cipriani and Noemi Kurt [2]\, we analyzed the decay of c
 orrelations for such fields with local pinning which is based on analytic 
 methods. Although the method does not use random walks\, it is actually cl
 ose in spirit to the methods using them. Presently\, the results are howev
 er much less precise than those obtained for gradient models.\n\nReference
 s\n\n[1] Bolthausen\, E.\, and Velenik\, Y.: Critical behavior of the mass
 less free field at the depinning transition. Commun. Math. Phys. 223\, 161
 -203 (2001).\n\n[2] Bolthausen\, E.\, Cipriani\, A.\, and Kurt\, N.: Expon
 ential Decay of Covari- ances for the Supercritical Membrane Model. Comm. 
 Math. Phys. 2017\, doi:10.1007/s00220-017-2886-x.
LOCATION:MR3\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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