Related papers: Stability criteria for q-expectation values
Based on the q-exponential distribution which has been observed in more and more physical systems, the varentropy method is used to derive the uncertainty measure of such an abnormal distribution function. The uncertainty measure obtained…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
We derive a generalized version of the work fluctuation theorem for nonequilibrium systems with spatio-temporal temperature fluctuations. For chi-square distributed inverse temperature we obtain a generalized fluctuation theorem based on…
Recently we have demostrated that the nonextensitivity parameter q occuring in some applications of Tsallis statistics (known also as index of the corresponding L\'evy distribution) is, in the q>1 case, given entirely by the fluctuations of…
Abelian non-topological solitons with Baryon and/or Lepton quantum numbers naturally appear in the spectrum of the minimal supersymmetric standard model. They arise as a consequence of the existence of flat directions in the potential…
The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they…
The classic central limit theorem and $\alpha$-stable distributions play a key role in probability theory, and also in Boltzmann-Gibbs (BG) statistical mechanics. They both concern the paradigmatic case of probabilistic independence of the…
Certain fluctuations in particle number at fixed total energy lead exactly to a cut-power law distribution in the one-particle energy, via the induced fluctuations in the phase-space volume ratio. The temperature parameter is expressed…
Dynamic equations concerning physical expectation values have been examined in terms of the real Hilbert space approach to quantum mechanics. The considered cases involve complex wave functions, as well as quaternionic wave functions. The…
The regularized signum-Gordon potential has a smooth minimum and is linear in the modulus of the field value for higher amplitudes. The Q-ball solutions in this model are investigated. Their existence for charges large enough is…
Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…
Chaos in classical systems has been studied in plenty over many years. Although the search for chaos in quantum systems has been an area of prominent research over the last few decades, the detailed analysis of many inherently chaotic…
We study p-adic counterparts of stable distributions, that is limit distributions for sequences of normalized sums of independent identically distributed p-adic-valued random variables. In contrast to the classical case, non-degenerate…
Hypothesis testing results often rely on simple, yet important assumptions about the behaviour of the distribution of p-values under the null and the alternative. We examine tests for one dimensional parameters of interest that converge to…
For a linear combination of random variables, fix some confidence level and consider the quantile of the combination at this level. We are interested in the partial derivatives of the quantile with respect to the weights of the random…
We discuss the analysis and stability of a family of cross-diffusion boundary value problems with nonlinear diffusion and drift terms. We assume that these systems are close, in a suitable sense, to a set of decoupled and linear problems.…
We discuss the relation between the quantum-mechanical survival probability of an unstable system in motion and that of the system at rest. The usual definition of the survival probability which takes into account only the time evolution of…
It is known that the nonextensive statistics was originally formulated for the systems composed of subsystems having same $q$. In this paper, the existence of composite system with different $q$ subsystems is investigated by fitting the…
In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the…
We consider the evolution and decay of Q-balls under the influence of quantum fluctuations. We argue that the most important effect resulting from these fluctuations is the modification of the effective potential in which the Q-ball…