Related papers: Benjamini-Schramm vs Plancherel convergence

In solar physics, especially in exploratory stages of research, it is often necessary to compare the power spectra of two or more time series. One may, for instance, wish to estimate what the power spectrum of the combined data sets might…

We investigate the spectral properties of balanced trees and dendrimers, with a view toward unifying and improving the existing results. Here we find a semi-factorized formula for their characteristic polynomials. Afterwards, we determine…

We observe that a large part of the volume of a hyperbolic polyhedron is taken by a tubular neighbourhood of its boundary, and use this to give a new proof for the finiteness of arithmetic maximal reflection groups following a recent work…

We show that our previous work on Galilei and Carroll gravity, apt for particles, can be generalized to Galilei and Carroll gravity theories adapted to p-branes (p = 0, 1, 2, ...). Within this wider brane perspective, we make use of a…

We consider the problem of learning regression functions from pairwise data when there exists prior knowledge that the relation to be learned is symmetric or anti-symmetric. Such prior knowledge is commonly enforced by symmetrizing or…

In this paper we prove coincidence results concerning spaces of absolutely summing multilinear mappings between Banach spaces. The nature of these results arises from two distinct approaches: the coincidence of two \textit{a priori}…

We prove the following for a bounded convex planar domain that is symmetric with respect to both coordinate axes. Consider a centered rectangle with sides parallel to the axes that strictly contains the domain. If the domain is not a…

We prove the Blaschke-Santal\'o inequality restricted to $n$-gons: the extremal polygons are the affine regular $n$-gons. If either the John or the L\"owner ellipse of a planar $o$-symmetric convex body $K$ is the unit circle about $o$,…

Random planar maps are considered in the physics literature as the discrete counterpart of random surfaces. It is conjectured that properly rescaled random planar maps, when conditioned to have a large number of faces, should converge to a…

It was recently claimed that the Planck length is not a limit to the precision by which we can measure distances, but that instead it is merely the Planck volume that limits the precision by which we can measure volumes. Here, we…

We improve the range of indices when the multilinear Bochner-Riesz means converges pointwisely. We obtain this result by establishing the $L^p$ estimates and weighted estimates of $k$-linear maximal Bochner-Riesz operators inductively,…

We prove a folklore conjecture that the Bergman measure along a holomorphic family of curves parametrized by the punctured unit disk converges to the Zhang measure on the associated Berkovich space. The convergence takes place on a…

We study Bernoulli$(p)$ percolation on (non)unimodular quasi-transitive graphs and prove that, almost surely, for any two heavy clusters $C$ and $C'$, the set of vertices in $C$ within distance one of $C'$ is light, i.e. it has finite total…

For a wide range of pairs of mixed norm spaces such that one space is contained in another, we characterize all cases when contractive norm inequalities hold. In particular, this yields such results for many pairs of weighted Bergman…

We prove several Stern's type congruences for generalized bernoulli numbers.

We study the weakest convergence-type conditions for fixed point results for Banach and Kannan mappings. Building on Suzuki's weakest condition for Banach mappings and our previous result for Kannan mappings, we compare convergence…

We prove that bounded Beltrami fields must be symmetric if a proportionality factor depends on 2 variables in the cylindrical coordinate and admits a regular level set diffeomorphic to a cylinder or a torus.

Thomas-Fermi model is considered here to make it cogent to capture the Planck-scale effect with the use of a generalization of uncertainty relation. Here generalization contains both linear and quadratic terms of momentum. We first…

We show by an example that the Demailly approximation sequence of a plurisubharmonic function, constructed via Bergman kernels, is not a decreasing sequence in general.

The convergence rates on polynomial interpolation in most cases are estimated by Lebesgue constants. These estimates may be overestimated for some special points of sets for functions of limited regularities. In this paper, by applying the…