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I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…
This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a functions of its summands as their number tends to infinity. The conditioning event is of moderate or…
A field theory with generalized statistics in one space dimension is introduced. The statistics enters the scene through the coupling of the matter fields to a statistical gauge field, as it happens in the Chern-Simons theory in two…
The multipole expansion is a key tool in the study of light-matter interactions. All the information about the radiation of and coupling to electromagnetic fields of a given charge-density distribution is condensed into few numbers: The…
Statistical thermodynamics is valuable as a conceptual structure that shapes our thinking about equilibrium thermodynamic states. A cloud of unresolved questions surrounding the foundations of the theory could lead an impartial observer to…
Filtered Poisson processes are often used as reference models for intermittent fluc- tuations in physical systems. Such a process is here extended by adding a noise term, either as a purely additive term to the process or as a dynamical…
In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term…
In a closed economic system, money is conserved. Thus, by analogy with energy, the equilibrium probability distribution of money must follow the exponential Gibbs law characterized by an effective temperature equal to the average amount of…
We study the continuum version of Sinai's problem of a random walker in a random force field in one dimension. A method of stochastic representations is used to represent various probability distributions in this problem (mean probability…
We give an equivalent condition for the existence of invariant Gibbs measures for sequences of continuous functions on one-sided subshifts and, more generally, for the existence of Gibbs measures. These extend the results of Kim [6] and…
Many events in biology are triggered when a diffusing searcher finds a target, which is called a first passage time (FPT). The overwhelming majority of FPT studies have analyzed the time it takes a single searcher to find a target. However,…
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…
The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…
The relation between continuous functions and random vectors is revealed in the paper that the main meaning is described as, for any given continuous function, there must be a sequence of probability spaces and a sequence of random vectors…
This article aims to introduced a new distribution named as extended xgamma (EXg) distribution. This generalization is derived from xgamma distribution (Xg), a special finite mixture of exponential and gamma distributions [see, Sen et al.…
An approach to the description of subdynamics inside non-relativistic quantum field theory is presented, in which the notions of relevant observable, time scale and complete positivity of the time evolution are stressed. A scattering theory…
Fundamental inconsistencies of superstatistics are highlighted. There is no such thing as a superposition of Boltzmann factors; what is actually derived is a generating function and not a normalizable probability density. The beta density…
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
Recent work has suggested that in highly correlated systems, such as sandpiles, turbulent fluids, ignited trees in forest fires and magnetization in a ferromagnet close to a critical point, the probability distribution of a global quantity…
The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…