Eigenvalue versus perimeter in a shape theorem for self-interacting random walks
Eigenvalue versus perimeter in a shape theorem for self-interacting random walks
We study paths of time-length $t$ of a continuous-time random walk on $\mathbb{Z}^{2}$ subject to self-interaction that depends on the geometry of the walk range and a collection of random, uniformly positive and finite edge weights. The interaction enters through a Gibbs weight at inverse temperature $\beta$; the “energy” is …