It is known that maximal entropy random walks and partition functions that count long paths
on graphs tend to become localized near nodes with a high degree. Here, we revisit the …

We study the asymptotic behavior of the number of paths of length N on several classes of
infinite graphs with a single special vertex. This vertex can work as an'entropic trap'for the …

I describe the manifestation of the non-Euclidean geometry in the behavior of collective
observables of some complex physical systems. Specifically, I consider the formation of …

A bstract We propose the holographic description of the Lifshitz tail typical for one-particle
spectral density of bounded disordered system in D= 1 space. To this aim the “polymer …

Collapse of the polymer chain upon the sharp decrease of solvent quality is studied. During
collapse, any pair of polymer units appearing in a sufficiently close vicinity in space has the …

It is known that maximal entropy random walks on graphs tend to get localized in the vicinity
of nodes with a large degree. Here we revisit the simplest toy model of such a localization-a …

Исследован коллапс полимерной цепи при скачкообразном ухудшении качества
растворителя. В процессе коллапса у любой пары звеньев полимера, оказавшихся на …