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 unrelat…
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…
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…
Math behind everyday life: "black days", their manifestation as traffic jams, and beyond
Daniil Fedotov, Sergei Nechaev
In our daily lives, we encounter numerous independent events, each occurring with varying probabilities over time. This letter delves into the scientific background behind the inho…