Related papers: Weak convergence implies convergence in mean withi…
We prove a $\Gamma$-convergence result for space dependent weak membrane energies, that is for 'truncated quadratic potentials', that are quadratic below some threshold (depending on the pair of points that we are considering) and constant…
The weak gravity conjecture (WGC) asserts that an Abelian gauge theory coupled to gravity is inconsistent unless it contains a particle of charge $q$ and mass $m$ such that $q \geq m/m_{\rm Pl}$. This criterion is obeyed by all known…
Using Monte Carlo simulation to calculate the Value at Risk (VaR) as a possible risk measure requires adequate techniques. One of these techniques is the application of a compound distribution for the aggregates in a portfolio. In this…
To prove that a measure, linearly representable by means of a finite set of nonnegative matrices $\mathcal M$, has the weak-Gibbs property, one check the uniform convergence (on $\mathcal M^\mathbb N$) of the sequence of vectors…
We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When…
The weak gravity conjecture (WGC) is an ultraviolet consistency condition asserting that an Abelian force requires a state of charge $q$ and mass $m$ with $q>m/m_{\rm Pl}$. We generalize the WGC to product gauge groups and study its tension…
The generalized extreme value distribution and its particular case, the Gumbel extreme value distribution, are widely applied for extreme value analysis. The Gumbel distribution has certain drawbacks because it is a non-heavy-tailed…
We revisit the problem of estimating the mean of a real-valued distribution, presenting a novel estimator with sub-Gaussian convergence: intuitively, "our estimator, on any distribution, is as accurate as the sample mean is for the Gaussian…
We develop a technique of multiple scale asymptotic expansions along mean flows and a corresponding notion of weak multiple scale convergence. These are applied to homogenize convection dominated parabolic equations with rapidly…
The Weak Gravity Conjecture (WGC) posits that gravity must be the weakest force in any consistent theory of quantum gravity. Originally formulated to constrain the landscape of effective field theories arising from string theory, the WGC…
This paper considers the mean variance portfolio management problem. We examine portfolios which contain both primary and derivative securities. The challenge in this context is due to portfolio's nonlinearities. The delta-gamma…
Gaussian belief propagation (GBP) is a recursive computation method that is widely used in inference for computing marginal distributions efficiently. Depending on how the factorization of the underlying joint Gaussian distribution is…
The Weak Gravity Conjecture (WGC) asserts a powerful consistency condition on gauge theories coupled to gravity, and it is widely believed that its proof will shed light on the quantum origin of gravitational interactions. Holography, and…
Recently, it has been proposed that the fundamental scale of quantum gravity can be close to the weak scale if there are large extra dimensions. This proposal has important phenomenological implications for processes at the TeV scale. We…
A random vector ${\bf X}$ is weakly stable iff for all $a,b\in \mathbb{R}$ there exists a random variable $\Theta$ such that $a{\bf X}+b{\bf X}'\stackrel{d}{=}{\bf X}\Theta$. This is equivalent (see \cite{MOU}) with the condition that for…
We introduce a faithful representation of the heavy tail multivariate distribution of asset returns, as parsimonous as the Gaussian framework. Using calculation techniques of functional integration and Feynman diagrams borrowed from…
For a contraction $C_0$-semigroup on a separable Hilbert space, the decay rate is estimated by using the weak Poincar\'e inequalities for the symmetric and anti-symmetric part of the generator. As applications, non-exponential convergence…
Geometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space.…
The purpose of this paper is to prove a weak convergence result for empirical processes indexed in general classes of functions and with an underlying $\alpha$-mixing sequence of random variables. In particular the uniformly boundedness…
We study the asymptotic properties, in the weak sense, of regenerative processes and Markov renewal processes. For the latter, we derive both renewal-type results, also concerning the related counting process, and ergodic-type ones,…