Rate of escape of the mixer chain.
Entropy of random walk range
We study the entropy of the set traced by an -step simple symmetric random walk on ℤ. We show that for ≥3, the entropy is of order . For =2, the entropy is of order /log2. These values are essentially governed by the size of the boundary of the trace.
Supercritical self-avoiding walks are space-filling
In this article, we consider the following model of self-avoiding walk: the probability of a self-avoiding trajectory between two points on the boundary of a finite subdomain of is proportional to . When is supercritical (i.e. where is the connective constant of the lattice), we show that the random trajectory becomes space-filling when taking the scaling limit.
Maximal arithmetic progressions in random subsets.
Random graph-homomorphisms and logarithmic degree.
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