Related papers: Conditions for the existence of a generalization o…
We present a variational characterization for the R\'{e}nyi divergence of order infinity. Our characterization is related to guessing: the objective functional is a ratio of maximal expected values of a gain function applied to the…
A novel general framework for the study of $\Gamma$-convergence of functionals defined over pairs of measures and energy-measures is introduced. This theory allows us to identify the $\Gamma$-limit of these kind of functionals by knowing…
The deformation principle admits one to obtain a very broad class of nonuniform geometries as a result of deformation of the proper Euclidean geometry. The Riemannian geometry is also obtained by means of a deformation of the Euclidean…
A differential algebra of nonlinear generalized functions is presented as a tool for a wide range of nonsmooth nonlinear problems. The power of the differential algebra is used to do mathematical calculations or proofs; then the final…
Let $\Omega\subsetneq\mathbb R^{n+1}$ be open and let $\mu$ be some measure supported on $\partial\Omega$ such that $\mu(B(x,r))\leq C\,r^n$ for all $x\in\mathbb R^{n+1}$, $r>0$. We show that if the harmonic measure in $\Omega$ satisfies…
We prove that every finite Borel measure $\mu$ in $\mathbb{R}^N$ that is bounded from above by the Hausdorff measure $\mathcal{H}^s$ can be split in countable many parts $\mu\lfloor_{E_k}$ that are bounded from above by the Hausdorff…
The method of exhaustion is generalized to a simple formula that can be used to integrate functions under very general conditions, provided that the integral exists. Both a geometric proof (following the usual procedure for the method of…
We prove an inversion theorem for the Fourier transform defined for normal functions, in the case when such functions are of moderate decrease, and in dimensions 2 and 3. This improves on Carleson's general almost everywhere convergence…
The generalized gamma distribution shows up in many problems related to engineering, hydrology as well as survival analysis. Earlier work has been done that estimated the deviation of the exponential and the Weibull distribution from…
We consider a large class of deformations of continuous and discrete biorthogonal ensembles and investigate their behavior in the limit of a large number of particles. We provide sufficient conditions to ensure that if a biorthogonal…
We present an extension of the deformation method applied to self-dual solutions of generalized Abelian Higgs-Chern-Simons models. Starting from a model defined by a potential $V(| \phi |)$ and a non-canonical kinetic term $\omega(| \phi |)…
In four dimensions complexified General Relativity (GR) can be non-trivially deformed: There exists an (infinite-parameter) set of modifications all having the same count of degrees of freedom. It is trivial to impose reality conditions…
This work explores properties of Strong Data-Processing constants for R\'enyi Divergences. Parallels are made with the well-studied $\varphi$-Divergences, and it is shown that the order $\alpha$ of R\'enyi Divergences dictates whether…
We show that to n loop order the divergent content of a Feynman amplitude is spanned by a set of basic (logarithmically divergent) integrals which need not be evaluated. Only the coefficients of the basic divergent integrals are necessary…
Let $A = \Bbbk Q / I$ be the path algebra of any finite quiver $Q$ modulo any two-sided ideal $I$ of relations and let $R$ be any reduction system satisfying the diamond condition for $I$. We introduce an intrinsic notion of deformation of…
A general divergence measure for monotonic functions is introduced. Its connections with the f-divergence for convex functions are explored. The main properties are pointed out.
One cannot justifiably presuppose the physical salience of structures derived via decoherence theory based upon an entirely uninterpreted use of the quantum formalism. Non-probabilistic accounts of the emergence of probability via…
We consider a sequence of random variables $(R_n)$ defined by the recurrence $R_n=Q_n+M_nR_{n-1}$, $n\ge1$, where $R_0$ is arbitrary and $(Q_n,M_n)$, $n\ge1$, are i.i.d. copies of a two-dimensional random vector $(Q,M)$, and $(Q_n,M_n)$ is…
We show that the absolute convergence of a Ramanujan expansion does not guarantee the convergence of its real variable generalization, which is obtained by replacing the integer argument in the Ramanujan sums with a real number. We also…
We construct explicitly deformations of Einstein's theory of gravity that are consistent and phenomenologically viable since they respect, in particular, cosmological backgrounds. We show that these deformations have unique symmetries in…