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Understanding the statistical behavior of the heat in stochastic systems gives us insight about the thermodynamics of such systems. Using the recently proposed Relativistic Stochastic Thermodynamics, we investigate the statistics of the…
We present a simple, pedagogical introduction to the statistics of extreme values. Motivated by a string of record high temperatures in December 1998, we consider the distribution, averages and lifetimes for a simplified model of such…
Bursty dynamics characterizes systems that evolve through short active periods of several events, which are separated by long periods of inactivity. Systems with such temporal heterogeneities are not only found in nature but also include…
We identify the conditions under which a stochastic driving inducing energy changes on a system coupled to a thermal bath can be treated as a work source. When these conditions are met, the work statistics satisfies the Crooks fluctuation…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
The gap in statistics between multi-variate and time-series analysis can be bridged by using entropy statistics and recent developments in multi-dimensional scaling. For explaining the evolution of the sciences as non-linear dynamics, the…
Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in…
In this note, we try to analyze and clarify the intriguing interplay between some counting problems related to specific thermalized weighted graphs and random walks consistent with such graphs.
As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…
We briefly review statistical models for the probability distribution of money developed in the econophysics literature since the late 1990s. In these models, economic transactions are modeled as random transfers of money between the agents…
These lectures describe several topics in statistical data analysis as used in High Energy Physics. They focus on areas most relevant to analyses at the LHC that search for new physical phenomena, including statistical tests for discovery…
Random walks on general graphs play an important role in the understanding of the general theory of stochastic processes. Beyond their fundamental interest in probability theory, they arise also as simple models of physical systems. A brief…
Discrete-time random walks and their extensions are common tools for analyzing animal movement data. In these analyses, resolution of temporal discretization is a critical feature. Ideally, a model both mirrors the relevant temporal scale…
Recently, progress has been made in the theory of turbulence, which provides a framework on how a deterministic process changes to a stochastic one owing to the change in thermodynamic states. It is well known that, in the framework of…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
Some stochastic systems are particularly interesting as they exhibit critical behavior without fine-tuning of a parameter, a phenomenon called self-organized criticality. In the context of driven-dissipative steady states, one of the main…
Ability of dynamical systems to relax to equilibrium has been investigated since the invention of statistical mechanics, which establishes the connection between dynamics of many-body Hamiltonian systems and phenomenological thermodynamics.…
Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention…
With the growing number of devices, sensors and digital systems, data logs may become uncertain due to, e.g., sensor reading inaccuracies or incorrect interpretation of readings by processing programs. At times, such uncertainties can be…
The past twenty years have seen a resurgence of interest in nonequilibrium thermodynamics, thanks to advances in the theory of stochastic processes and in their thermodynamic interpretation. Fluctuation theorems provide fundamental…