TY - JOUR
T1 - Scaling limits for non-intersecting polymers and Whittaker measures
AU - Johnston, Samuel
AU - O'Connell, Neil
PY - 2020/10/2
Y1 - 2020/10/2
N2 - We study the partition functions associated with non-intersecting polymers in a random environment. By considering paths in series and in parallel, the partition functions carry natural notions of subadditivity, allowing the effective study of their asymptotics. For a certain choice of random environment, the geometric RSK correspondence provides an explicit representation of the partition functions in terms of a stochastic interface. Formally this leads to a variational description of the macroscopic behaviour of the interface and hence the free energy of the associated non-intersecting polymer model. At zero temperature we relate this variational description to the Marčenko–Pastur distribution, and give a new derivation of the surface tension of the bead model.
AB - We study the partition functions associated with non-intersecting polymers in a random environment. By considering paths in series and in parallel, the partition functions carry natural notions of subadditivity, allowing the effective study of their asymptotics. For a certain choice of random environment, the geometric RSK correspondence provides an explicit representation of the partition functions in terms of a stochastic interface. Formally this leads to a variational description of the macroscopic behaviour of the interface and hence the free energy of the associated non-intersecting polymer model. At zero temperature we relate this variational description to the Marčenko–Pastur distribution, and give a new derivation of the surface tension of the bead model.
U2 - 10.1007/s10955-020-02534-y
DO - 10.1007/s10955-020-02534-y
M3 - Article
SN - 0022-4715
VL - 179
SP - 354
EP - 407
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
ER -