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SUMMARY:Polymer pinning with sparse disorder - Professor Ken Alexander\, U
 niversity of Southern California
DTSTART:20140520T140000Z
DTEND:20140520T150000Z
UID:TALK52668@talks.cam.ac.uk
CONTACT:37296
DESCRIPTION:The standard setup in disordered pinning models is that a poly
 mer configuration is modeled by the trajectory of a Markov chain which is 
 rewarded or penalized by an amount \\omega_n when it returns to a special 
 state 0 at time n.  More precisely\, for a polymer of length N the Boltzma
 nn weight is e^{\\beta H}\, where for a trajectory \\tau\, H(\\tau) is the
  sum of the values \\omega_n at the times n \\leq N of the returns to 0 of
  \\tau.  Typically the \\omega_n are taken to be a quenched realization of
  a iid sequence\, but here we consider the case of sparse disorder: \\omeg
 a_n is 1 at the returns times of a quenched realization of a renewal seque
 nce \\{\\sigma_j\\}\, and 0 otherwise\; in the interesting cases the gaps 
 between renewals have infinite mean\, and we assume the gaps have a regula
 rly varying power-law tail.  For \\beta above a critical point\, the polym
 er is pinned in the sense that \\tau asymptotically hits a positive fracti
 on of the N renewals in \\sigma.  To see the effect of the disorder one ca
 n compare this critical point to the one in the corresponding annealed sys
 tem.  We establish equality or inequality of these critical points dependi
 ng on the sum of the tail exponents of the two renewal sequences (that is\
 , \\sigma and the return times of \\tau.)  This is joint work with Quentin
  Berger.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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