Related papers: G-casual Stable Probability Distributions
We consider a system of weak* closed sets of finite-dimensional distributions. We show that a corresponding system of random variables can be defined on a probability space with a probability measure determined up to some set of measures,…
Sums of independent, bounded random variables concentrate around their expectation approximately as well a Gaussian of the same variance. Well known results of this form include the Bernstein, Hoeffding, and Chernoff inequalities and many…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
Symmetric heavily tailed random walks on $Z^d, d\geq 1,$ are considered. Under appropriate regularity conditions on the tails of the jump distributions, global (i.e., uniform in $x,t, |x|+t\to\infty,$) asymptotic behavior of the transition…
We consider several notions of genericity appearing in algebraic geometry and commutative algebra. Special emphasis is put on various stability notions which are defined in a combinatorial manner and for which a number of equivalent…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
Concerning Numerical Stochastic Perturbation Theory, we discuss the convergence of the stochastic process (idea of the proof, features of the limit distribution, rate of convergence to equilibrium). Then we also discuss the expected…
In the stable marriage problem N men and N women have to be matched by pairs under the constraint that the resulting matching is stable. We study the statistical properties of stable matchings in the large N limit using both numerical and…
General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…
In this paper, we focus on the analysis of discrete versions of the Calderon problem with partial boundary data in dimension d >= 3. In particular, we establish logarithmic stability estimates for the discrete Calderon problem on an…
This paper deals with a one--dimensional model for granular materials, which boils down to an inelastic version of the Kac kinetic equation, with inelasticity parameter $p>0$. In particular, the paper provides bounds for certain distances…
This paper examines the classical matching distribution arising in the "problem of coincidences". We generalise the classical matching distribution with a preliminary round of allocation where items are correctly matched with some fixed…
In this paper, we define and study a new notion of stability for the $k$-means clustering scheme building upon the notion of quantization of a probability measure. We connect this notion of stability to a geometric feature of the underlying…
We develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations…
We consider the problem of distribution-free predictive inference, with the goal of producing predictive coverage guarantees that hold conditionally rather than marginally. Existing methods such as conformal prediction offer marginal…
In nature or societies, the power-law is present ubiquitously, and then it is important to investigate the mathematical characteristics of power-laws in the recent era of big data. In this paper we prove the superposition of non-identical…
In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.
We develop several aspects of local and global stability in continuous first order logic. In particular, we study type-definable groups and genericity.