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Diffusion models have made remarkable progress in solving various inverse problems, attributing to the generative modeling capability of the data manifold. Posterior sampling from the conditional score function enable the precious data…
Einstein's explanation of Brownian motion provided one of the cornerstones which underlie the modern approaches to stochastic processes. His approach is based on a random walk picture and is valid for Markovian processes lacking long-term…
Emergence is a concept that is easy to exhibit, but very hard to formally handle. This paper is about cubic sand grains moving around on nicely packed columns in one dimension (the physical sandpile is two dimensional, but the support of…
We introduce a new mechanism that produces a Hall-like response in time-reversal-invariant materials, driven entirely by geometric effects. Specifically, we demonstrate that a tilted potential interface causes electron wave packets to…
In this paper we consider a model of spreading information in heterogeneous systems wherein we have two kinds of objects. Some of them are active and others are passive. Active objects can, if they possess information, share it with an…
The spread of the time arrows from the environment to an observed subsystem is followed within a harmonic model. A similarity is pointed out between irreversibility and a phase with spontaneously broken symmetry. The causal structure of…
Archetypal falling behaviors of impervious objects are classified into four modes: fluttering, tumbling, steady descent and chaotic motion. The classical scenario predicts these behaviors to be affected by two dimensionless quantities:…
Turbulence is ubiquitous in plasmas, leading to rich dynamics characterized by irregularity, irreversibility, energy fluctuations across many scales, and energy transfer across many scales. Another fundamental and generic feature of…
In many-particle diffusions, particles that move the furthest and fastest can play an outsized role in physical phenomena. A theoretical understanding of the behavior of such extreme particles is nascent. A classical model, in the spirit of…
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…
We present a Master Equation formulation based on a Markovian random walk model that exhibits sub-diffusion, classical diffusion and super-diffusion as a function of a single parameter. The non-classical diffusive behavior is generated by…
Via large-scale molecular dynamics simulations, we observe the melting of a topological glass of stiff ring polymers by incorporating flexible ring polymers, along an isobaric path. As more flexible ring polymers are introduced, cluster…
Hyperbolic (or indefinite) materials have attracted significant attention due to their unique capabilities for engineering electromagnetic space and controlling light propagation. A current challenge is to find a hyperbolic material with…
A notion of random walks for circle packings is introduced. The geometry behind this notion is discussed, together with some applications. In particular, we obtain a short proof of a result regarding the type problem for circle packings,…
Diffusion models have become increasingly popular for generative modeling due to their ability to generate high-quality samples. This has unlocked exciting new possibilities for solving inverse problems, especially in image restoration and…
"Oscillations" occur in quite different kinds of many-particle-systems when two groups of particles with different directions of motion meet or intersect at a certain spot. We present a model of pedestrian motion that is able to reproduce…
The diffusion of astrophysical magnetic fields in conducting fluids in the presence of turbulence depends on whether magnetic fields can change their topology or reconnect in highly conducting media. Recent progress in understanding fast…
We introduce a diffusion model for energetically inhomogeneous systems. A random walker moves on a spin-S Ising configuration, which generates the energy landscape on the lattice through the nearest-neighbors interaction. The underlying…
Intriguing analogies were found between a model of plastic deformation in crystals and turbulence in fluids. A study of this model provides remarkable explanations of known experiments and predicts fractal dislocation pattern formation.…
The cover-time problem, i.e., time to visit every site in a system, is one of the key issues of random walks with wide applications in natural, social, and engineered systems. Addressing the full distribution of cover times for random walk…