Related papers: Relations between exponential tails, moments and m…
The right tail asymptotic series consisting of attenuating exponential terms are derived for the densities of Galton-Watson processes with fractional probability generating functions. The frequencies in the exponential factors form fractal…
In this paper non-asymptotic exponential estimates are derived for the tail distribution of polynomial martingale differences in terms unconditional tails distributions of summands. Applications are considered in the theory of polynomials…
We study the probability density function for the fluctuations of the magnetic order parameter in the low temperature phase of the XY model of finite size. In two-dimensions this system is critical over the whole of the low temperature…
In previous work Majda and McLaughlin computed explicit expressions for the $2N$th moments of a passive scalar advected by a linear shear flow in the form of an integral over ${\bf R}^N$. In this paper we first compute the asymptotics of…
In transport processes across materials like glasses, living cells, and porous media, the probability density function of displacements exhibits exponential decay rather than Gaussian behavior. We show that this universal behavior of rare…
We study branching processes of independently splitting particles in the continuous time setting. If time is calibrated such that particles live on average one unit of time, the corresponding transition rates are fully determined by the…
We study the one-dimensional branching random walk in the case when the step size distribution has a stretched exponential tail, and, in particular, no finite exponential moments. The tail of the step size $X$ decays as $\mathbb{P}[X \geq…
We examine random variables in the power law/regularly varying class with stochastic tail exponent, the exponent $\alpha$ having its own distribution. We show the effect of stochasticity of $\alpha$ on the expectation and higher moments of…
Similar to the associated Legendre functions, the differential equation for the associated Bessel functions $B_{l,m}(x)$ is introduced so that its form remains invariant under the transformation $l\rightarrow -l-1$. A Rodrigues formula for…
Using an Eulerian perturbative calculation, we show that the distribution of relative pairwise velocities which arises from gravitational instability of Gaussian density fluctuations has asymmetric (skewed) exponential tails. The negative…
We present in this document the Lebesgue and Sobolev propagation of exponential tails for solutions of the homogeneous Boltzmann equation for hard and Maxwell interactions. In addition, we show the $L^{p}$-integrability creation of such…
Due to globalization and relaxed market regulation, we have assisted to an increasing of extremal dependence in international markets. As a consequence, several measures of tail dependence have been stated in literature in recent years,…
We study the Central Limit Theorem (CLT) in the so-called mixed (anisotropic) Lebesgue-Riesz spaces and tail behavior of normed sums of centered random independent variables (vectors) with values in these spaces.
We consider branching random walks on the Euclidean lattice in dimensions five and higher. In this non-Markovian setting, we first obtain a relationship between the equilibrium measure and Green's function, in the form of an approximate…
In this note we prove bounds on the upper and lower probability tails of sums of independent geometric or exponentially distributed random variables. We also prove negative results showing that our established tail bounds are asymptotically…
We derive exponential bounds for tail of distribution for natural, i.e. under ordinary logarithm, normalized sums of arrays of random variables, not necessarily independent.
We derive exponential tail inequalities for sums of random matrices with no dependence on the explicit matrix dimensions. These are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
We study behavior of a measure on $[0,\infty)$ by considering its Laplace transform. If it is possible to extend the Laplace transform to a complex half-plane containing the imaginary axis, then the exponential decay of the tail of the…
This paper investigates the asymptotic behavior of higher-order conditional tail moments, which quantify the contribution of individual losses in the event of systemic collapse. The study is conducted within a framework comprising two…