Related papers: Clustering of large deviations in moving average p…
Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…
Clustering large, mixed data is a central problem in data mining. Many approaches adopt the idea of k-means, and hence are sensitive to initialisation, detect only spherical clusters, and require a priori the unknown number of clusters. We…
Identifying and quantifying memory are often critical steps in developing a mechanistic understanding of stochastic processes. These are particularly challenging and necessary when exploring processes that exhibit long-range correlations.…
Although higher-order interactions are known to affect the typical state of dynamical processes giving rise to new collective behavior, how they drive the emergence of rare events and fluctuations is still an open problem. We investigate…
The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…
We present large-scale molecular dynamics simulations to study the free evolution of granular gases. Initially, the density of particles is homogeneous and the velocity follows a Maxwell-Boltzmann (MB) distribution. The system cools down…
The timing patterns of human communication in social networks is not random. On the contrary, communication is dominated by emergent statistical laws such as non-trivial correlations and clustering. Recently, we found long-term correlations…
This work is a continuation of the manuscript "the structure of extreme level sets in branching Brownian motion", in which the same authors studied the fine structure of the extreme level sets of branching Brownian motion, namely the sets…
Despite the inherent lack of a ground truth in clustering, a broad consensus is overall acknowledged in defining the concept of cluster in the continuous setting. Conversely, this remains controversial in the presence of categorical data.…
We study large deviation probabilities for a sum of dependent random variables from a heavy-tailed factor model, assuming that the components are regularly varying. We identify conditions where both the factor and the idiosyncratic terms…
We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological…
Brownian motion is ballistic on short time scales and diffusive on long time scales. Our theoretical investigations indicate that one can observe the exact opposite - an "anomaleous diffusion process" where initially diffusive motion…
Clustering is one of the most fundamental and wide-spread techniques in exploratory data analysis. Yet, the basic approach to clustering has not really changed: a practitioner hand-picks a task-specific clustering loss to optimize and fit…
We consider a cluster growth model on the d-dimensional lattice, called internal diffusion limited aggregation (internal DLA). In this model, random walks start at the origin, one at a time, and stop moving when reaching a site not occupied…
Using high precision Monte Carlo simulations and a mean-field theory, we explore coarsening phenomena in a simple driven diffusive system. The model is reminiscent of vehicular traffic on a two-lane ring road. At sufficiently high density,…
The evolution of tokens through deep transformer models can be modeled as an interacting particle system that has been shown to exhibit an asymptotic clustering behavior akin to the synchronization phenomenon in Kuramoto models. In this…
Cyclically sheared jammed packings form memories of the shear amplitude at which they were trained by falling into periodic orbits where each particle returns to the identical position in subsequent cycles. While simple models that treat…
The properties of small clusters can differ dramatically from the bulk phases of the same constituents. In equilibrium, cluster assembly has been recently explored, whereas out of equilibrium, the physical principles of clustering remain…
We study the problem of learning clusters of partially observed linear dynamical systems from multiple input-output trajectories. This setting is particularly relevant when there are limited observations (e.g., short trajectories) from…
We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers…