相关论文: Quantization from an exponential distribution of i…

One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a…

Predicting extreme events in nonlinear dynamical systems is challenging due to a limited understanding of their statistical properties. This study numerically and theoretically investigates the statistical properties of infinite-modal maps…

We examine the stationary distribution of random walks on directed graphs. In particular, we focus on the {\em principal ratio}, which is the ratio of maximum to minimum values of vertices in the stationary distribution. We give an upper…

Anomalous diffusion and power-law distributions are observed in various complex systems. To provide a consistent dynamical foundation for these phenomena, we present a geometric derivation of the nonlinear Fokker-Planck equation by…

We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…

A statistical measure is given expressing relative occurrences of quantities within a given data set. Application of this measure on several real life physical data sets and some abstract distributions are shown to yield consistent results.…

In this work we present the fundamental ideas of inference over paths, and show how this formalism implies the continuity equation, which is central for the derivation of the main partial differential equations that constitute…

Entropic dynamics, a program that aims at deriving the laws of physics from standard probabilistic and entropic rules for processing information, is developed further. We calculate the probability for an arbitrary path followed by a system…

Time evolutions whose infinitesimal generator is a fractional time derivative arise generally in the long time limit. Such fractional time evolutions are considered here for random walks. An exact relationship is given between the…

We advance the previous studies of quantum walks on the line with two coins. Such four-state quantum walks driven by a three-direction shift operator may have nonzero stationary distributions (localization), thus distinguishing themselves…

Focusing on a continuous-time quantum walk on $\mathbb{Z}=\left\{0,\pm 1,\pm 2,\ldots\right\}$, we analyze a probability distribution with which the quantum walker is observed at a position. The walker launches off at a localized state and…

When the data do not conform to the hypothesis of a known sampling-variance, the fitting of a constant to a set of measured values is a long debated problem. Given the data, fitting would require to find what measurand value is the most…

Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have influence of a universal sort and manifest themselves in scaling…

A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…

We present certain mathematical aspects of an information method which was formulated in an attempt to investigate diffusion phenomena. We imagine a regular dynamical hamiltonian systems under the random perturbation of thermal (molecular)…

The exponent of anomalous diffusion of virus in cytoplasm of a living cell is experimentally known to fluctuate depending on localized areas of the cytoplasm, indicating heterogeneity of diffusion. In a recent paper (Itto, 2012), a…

We study the motion of a massive particle in a quenched random environment at zero temperature. The distribution of particle positions is investigated numerically and special focus is placed on the mean stopping distance and its…

Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related…

We present a method for incorporating a stochastic point of view into physics exercises of mathematics education. The core of our method is the randomization of some inputs, the system model used does not differ from what we would use in…

Let $(X,Y)$ be a bivariate random vector. The estimation of a probability of the form $P(Y\leq y \mid X >t) $ is challenging when $t$ is large, and a fruitful approach consists in studying, if it exists, the limiting conditional…