Related papers: L\'evy group and density measures
In this article we generalize the classical Edgeworth expansion for the probability density function (PDF) of sums of a finite number of symmetric independent identically distributed random variables with a finite variance to sums of…
We prove that for certain actions of a discrete countable residually finite amenable group acting on a compact metric space with specification property, periodic measures are dense in the set of invariant measures.
Belinschi et al. [Adv. Math., 226 (2011), 3677--3698] proved that the normal distribution is freely infinitely divisible. This paper establishes a certain monotonicity, real analyticity and asymptotic behavior of the density of the free…
In this paper we study satisfiability of random equations in an infinite finitely generated nilpotent group G. We show that the set SAT(G,k) of all equations in k > 1 variables over G which are satisfiable in G has an intermediate…
We study the relative growth of finitely generated subgroups in finitely generated groups, and the corresponding distortion function of the embeddings. We explore which functions are equivalent to the relative growth functions and…
Given a low frequency sample of an infinitely divisible moving average random field $\{\int_{\mathbb{R}^d} f(x-t)\Lambda(dx); \ t \in \mathbb{R}^d \}$ with a known simple function $f$, we study the problem of nonparametric estimation of the…
Loop groups G as families of mappings of the complex manifold M into another complex manifold N preserving marked points $s_0\in M$ and $y_0\in N$ are investigated. Quasi-invariant measures $\mu $ on G relative to dense subgroups $G'$ are…
L\'{e}vy walks are a particular type of continuous-time random walks which results in a super-diffusive spreading of an initially localized packet. The original one-dimensional model has a simple schematization that is based on starting a…
The functions $F_{G}(n)$ measures the asymptotic behavior of residual finiteness for a finitely generated group $G$. In previous work \cite{Pengitore_1}, the author claimed a characterization for $F_{N}(n)$ when $N$ is a finitely generated…
Given a free additive convolution semigroup $\left(\mu_t\right)_{t\geq 0}$ and a probability measure $\nu$ on $\mathbb{R}$, we find the necessary and sufficient conditions for the process $\mu_t \boxplus \nu$ to be Lebesgue absolutely…
We give sufficient conditions for the asymptotic normality of linear combinations of order statistics (L-statistics) in the case of simple random samples without replacement. In the first case, restrictions are imposed on the weights of…
For every non-hyper-FC-central countable amenable group and every $k\geq 2$, we provide a sequence of symmetric, fully supported probability measures such that their convex combination is non-Liouville (that is it admits a non-constant…
We develop a new method for studying the asymptotics of symmetric polynomials of representation-theoretic origin as the number of variables tends to infinity. Several applications of our method are presented: We prove a number of theorems…
We study an analogue of the large deviation principle for mixed measures associated with a class of $\log$-concave probability measures whose densities depend on the gauge function of a convex body. For convex bodies in $\mathbb{R}^n$, we…
Symbolic dynamical theory plays an important role in the research of amenability with a countable group. Motivated by the deep results of Dougall and Sharp, we study the group extensions for topologically mixing random shifts of finite…
For random piecewise linear systems T of the interval that are expanding on average we construct explicitly the density functions of absolutely continuous T-invariant measures. In case the random system uses only expanding maps our…
A topological group $G$ is said to have the L\'evy property if it admits a dense subgroup which is decomposed as the union of an increasing sequence of compact subgroups $\mathcal{G}=\{G_i:i\in\mathbb{N}\}$ of $G$ which exhibits…
In this paper we provide sufficient conditions which guarantee the existence of a system of invariant measures for semigroups associated to systems of parabolic differential equations with unbounded coefficients. We prove that these…
In this paper we investigate the relation between measure expansiveness and hyperbolicity. We prove that non atomic invariant ergodic measures with all of its Lyapunov exponents positive is positively measure-expansive. We also prove that…
A L{\'e}vy walk of order $\beta$ is studied on an interval of length $L$, driven out of equilibrium by different-density boundary baths. The anomalous current generated under these settings is nonlocally related to the density profile…