4 papers
Three faces of random walks in hyperbolic domain: BKT, Lifshitz tails, and KPZ
Daniil Fedotov, Sergei Nechaev
We show that continuous random walks (diffusion) in the Poincaré hyperbolic upper halfplane provide a unifying description of three seemingly unrela…
Non-algebraic first return probability of a stretched random walk near a convex boundary and its effect on adsorption
Daniil Fedotov, Sergei Nechaev
The -step random walk, elongated in the vicinity of a disc (in 2D) or a sphere (in 3D) of radius , demonstrates a non-algebraic stretched exponential decay $P_N\sim \exp\left…
Collective communication in a transparent world: Phase transitions in a many-body Potts model and social-quantum duality
Pawat Akara-pipattana, Sergei Nechaev, Bogdan Slavov
Digitally connected societies approach a \enquote{transparent} regime where all agents can interact without geographic or social barriers -- a limit realized by complete graph topo…
KPZ-like scaling on a high-dimensional hypersphere
Daniil Fedotov, Sergei Nechaev
We consider the orientational diffusion controlled by the hyperspherical Laplacian, , on the surface of the --dimensional hypersphere in the limit . We…