Related papers: Generalised cascades
This paper offers a brief introduction to the framework of "general probabilistic theories", otherwise known as the "convex-operational" approach the foundations of quantum mechanics. Broadly speaking, the goal of research in this vein is…
The generalized entropic measure, which is optimized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered and its…
The stochastic properties of variables whose addition leads to $q$-Gaussian distributions $G_q(x)=[1+(q-1)x^2]_+^{1/(1-q)}$ (with $q\in\mathbb{R}$ and where $[f(x)]_+=max\{f(x),0\}$) as limit law for a large number of terms are…
We propose a general approach, named by us hyperstatistics, to treat complex systems, in which Boltzmann-Gibbs statistics breaks down in domains of the system. Hyperstatistics preserves the concavity of nonadditive $q$-entropy. We obtain…
Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. Here we consider generalised Bayesian…
The familiar cascade measures are sequences of random positive measures obtained on $[0,1]$ via $b$-adic independent cascades. To generalize them, this paper allows the random weights invoked in the cascades to take real or complex values.…
New formulations of quantum generalized fluctuation-dissipation relations in terms of characteristic and probabilistic functionals of continuous observations are suggested and discussed. It is shown that control of entropy production in…
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…
A class of discrete distributions can be derived from stationary renewal processes. They have the useful property that the mean is a simple function of the model parameters. Thus regressions of the distribution mean on covariates can be…
We establish new product identities involving the $q$-analogue of the Fibonacci numbers. We show that the identities lead to alternate expressions of generating functions for close-packed dimers on non-orientable surfaces.
Statistical mechanics is generalized on the basis of an information theory for inexact or incomplete probability distributions. A parameterized normalization is proposed and leads to a nonextensive entropy. The resulting incomplete…
It is by now well known that the Boltzmann-Gibbs (BG) entropy $S_{BG}=-k\sum_{i=1}^W p_i \ln p_i$ can be usefully generalized into the entropy $S_q=k (1-\sum_{i=1}^Wp_i^{q}) / (q-1)$ ($q\in \mathcal{R}; S_1=S_{BG}$). Microscopic dynamics…
This work develops a quantitative homogenization theory for random suspensions of rigid particles in a steady Stokes flow, and completes recent qualitative results. More precisely, we establish a large-scale regularity theory for this…
A generalized definition of average, termed the q-average, is widely employed in the field of nonextensive statistical mechanics. Recently, it has however been pointed out that such an average value may behave unphysical under specific…
We introduce a new permutation statistic, namely, the number of cycles of length $q$ consisting of consecutive integers, and consider the distribution of this statistic among the permutations of $\{1,2,...,n\}$. We determine explicit…
For a general family of non-negative functions matching upper and lower bounds are established for their average over the values of any equidistributed sequence.
Recent investigations of turbulent circulation fluctuations have uncovered substantial insights into the statistical organization of flow structures and revealed unexpected geometric features of turbulent intermittency. Of particular…
In this work we present a natural generalization of strong pseudoprime to base $b$, which we have called $q$-pseudoprime to base $b$. It allows us to present another way to define a Midy's number to base $b$ (overpseudoprime to base $b$).…
We have found an analytic expression for the multivariate generating function governing all n-point statistics of random multiplicative cascade processes. The variable appropriate for this generating function is the logarithm of the energy…
We establish an abstract quenched linear response result for random dynamical systems, which we then apply to the case of smooth expanding on average cocycles on the unit circle. In sharp contrast to the existing results in the literature,…