Related papers: Heavy-tailed Distributions In Stochastic Dynamical…

Statistical description of stochastic dynamics in highly unstable potentials is strongly affected by properties of divergent trajectories, that quickly leave meta-stable regions of the potential landscape and never return. Using ideas from…

Heavy-tailed phenomena appear across diverse domains --from wealth and firm sizes in economics to network traffic, biological systems, and physical processes-- characterized by the disproportionate influence of extreme values. These…

Extreme events are an important theme in various areas of science because of their typically devastating effects on society and their scientific complexities. The latter is particularly true if the underlying dynamics does not lead to…

We develop a general approach for studying the cumulative probability distribution function of localized objects (particles) whose dynamics is governed by the first-order Langevin equation driven by superheavy-tailed noise. Solving the…

Temporal sequences of discrete events that describe natural and social processes are often driven by non-Poisson dynamics. In addition to a heavy-tailed interevent time distribution, which primarily captures the deviation from a Poisson…

Since the turn of the century, there has been increased interest in the application of heavy-tailed distributions, particularly stable distributions, to problems in physics and finance. Although, the tails of stable distributions provide a…

Synaptic plasticity typically produces heavy-tailed distributions of synaptic strengths, consisting of a few strong connections among many weaker ones. Meanwhile, structural plasticity relies on distinct signaling cascades to reshape…

Power-law tails are ubiquitous in income distributions and in the energy distributions of diluted relativistic gases. We analyze the conceptual link between these two cases. In economic interactions fat tails arise because the richest…

The dominant approaches to text representation in natural language rely on learning embeddings on massive corpora which have convenient properties such as compositionality and distance preservation. In this paper, we develop a novel method…

Stochastic dominance of a random variable by a convex combination of its independent copies has recently been shown to hold within the relatively narrow class of distributions with concave odds function, and later extended to broader…

Quantitative understanding of human behaviors provides elementary comprehension of the complexity of many human-initiated systems. A basic assumption embedded in the previous analyses on human dynamics is that its temporal statistics are…

Heavy tails are often found in practice, and yet they are an Achilles heel of a variety of mainstream random probability measures such as the Dirichlet process (DP). The first contribution of this paper focuses on characterizing the tails…

Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized…

Beck et al. (2013) introduced a new distribution class J which contains many heavy-tailed and light-tailed distributions obeying the principle of a single big jump. Using a simple transformation which maps heavy-tailed distributions to…

We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable L\'evy distribution; it is assumed as a jumping process (the kangaroo…

The analysis in this paper helps to explain the formation of growing networks with degree distributions that follow extended exponential or power-law tails. We present a generic model in which edge dynamics are driven by a continuous…

The size that an epidemic can reach, measured in terms of the number of fatalities, is an extremely relevant quantity. It has been recently claimed [Cirillo & Taleb, Nature Physics 2020] that the size distribution of major epidemics in…

We consider Stochastic Volatility processes with heavy tails and possible long memory in volatility. We study the limiting conditional distribution of future events given that some present or past event was extreme (i.e. above a level which…

Continuous mixtures of distributions are widely employed in the statistical literature as models for phenomena with highly divergent outcomes; in particular, many familiar heavy-tailed distributions arise naturally as mixtures of…

Heavy-tailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closed-form in graphical models which involve such heavy-tailed distributions. In this work, we…