Related papers: Renewal and memory properties in the random growth…

Motivated by recent experimental studies in microbiology, we suggest a modification of the classic ballistic deposition model of surface growth, where the memory of a deposition at a site induces more depositions at that site or its…

Stochastic renewal processes are ubiquitous across physics, biology, and the social sciences. Here, we show that continuous-time renewal dynamics can naturally produce a mixed discrete-continuous structure, with a macroscopic fraction of…

A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in $(1 + 1)$ dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton…

Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits…

Active systems across scales, ranging from molecular machines to human crowds, are usually modeled as assemblies of self-propelled particles driven by internally generated forces. However, these models often assume memoryless dynamics and…

We propose a new self-organizing mechanism behind the emergence of memory in which temporal sequences of stimuli are transformed into spatial activity patterns. In particular, the memory emerges despite the absence of temporal correlations…

Diffusion models power leading generative AI, but when and how they memorize training data, especially on low-dimensional manifolds, remains unclear. We find memorization emerges gradually, not abruptly: as data become scarce, diffusion…

Direct reciprocity is a mechanism for the evolution of cooperation in repeated social interactions. According to this literature, individuals naturally learn to adopt conditionally cooperative strategies if they have multiple encounters…

There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…

We consider two different proposals to generate a time series with the same non-Poisson distribution of waiting times, to which we refer to as renewal and modulation. We show that, in spite of the apparent statistical equivalence, the two…

We explore the concept of memory in scalar active matter, focusing on the collective dynamics of particles whose interactions depend on their evolutionary history rather than solely on their current configuration. We introduce the idea of…

We consider the drift and diffusion properties of periodically driven renewal processes. These processes are defined by a periodically time dependent waiting time distribution, which governs the interval between subsequent events. We show…

We study the emergence of correlations between $N$ components of the position of a diffusive walker in $N$ dimensions that starts at the origin and resets to previously visited sites with certain probabilities. This is equivalent to $N$…

Generative diffusion models have emerged as powerful tools for sampling high-dimensional distributions, yet they typically rely on white gaussian noise and noise schedules to destroy and reconstruct information. Here, we demonstrate that…

We consider a continuous-space and continuous-time diffusion process under resetting with memory. A particle resets to a position chosen from its trajectory in the past according to a memory kernel. Depending on the form of the memory…

We consider renewal stochastic processes generated by non-independent events from the perspective that their basic distribution and associated generating functions obey the statistical-mechanical structure of systems with interacting…

Renewal theory is finding increasing applications in non-equilibrium statistical physics. One example relates the probability density and survival probability of a Brownian particle or an active run-and-tumble particle with stochastic…

The generative process of Diffusion Models (DMs) has recently set state-of-the-art on many AI generation benchmarks. Though the generative process is traditionally understood as an "iterative denoiser", there is no universally accepted…

We show numerically that a three-dimensional model for structural glass displays aging, rejuvenation and memory effects when submitted to a temperature cycle. These effects indicate that the free energy landscape of structural glasses may…

The growth of a tissue, which depends on cell-cell interactions and biologically relevant process such as cell division and apoptosis, is regulated by a mechanical feedback mechanism. We account for these effects in a minimal…