Related papers: Around Brody lemma
The Lindy effect is a statistical tendency for things with longer pasts behind them to have longer futures ahead. It has been experimentally confirmed to apply to some categories, but not others, raising questions about when it is…
We study several consequences of the packing problem, a conjecture from combinatorial optimization, using algebraic invariants of square-free monomial ideals. While the packing problem is currently unresolved, we successfully settle the…
Sequences of discrete random variables are studied whose probability generating functions are zero-free in a sector of the complex plane around the positive real axis. Sharp bounds on the cumulants of all orders are stated, leading to…
We give an example of a projective manifold with dense entire curves such that every Brody curve is degenerate.
We consider transient nearest neighbor random walks on the positive part of the real line. We give criteria for the finiteness of the number of cutpoints and strong cutpoints. Examples and open problems are presented.
We survey elementary results in Minkowski spaces (i.e. finite dimensional Banach spaces) that deserve to be collected together, and give simple proofs for some of them. We place special emphasis on planar results. Many of these results have…
We establish the connection between the Steinitz problem for ordering vector families in arbitrary norms and its variant for not necessarily zero-sum families consisting of `nearly unit' vectors.
We construct direct and inverse systems of Minkowski's balls and domains, direct and inverse systems of their critical lattices and calculate their direct and inverse limits.
We survey three results on syzygies of curves beyond Green's conjecture, with a particular emphasis on drawing connections between the study of syzygies and other topics in moduli theory.
This short note, in part of expository nature, points out several new or recent consequences of a quite nice decomposition for positive semi-definite matrices.
Mediation analysis is difficult when the number of potential mediators is larger than the sample size. In this paper we propose new inference procedures for the indirect effect in the presence of high-dimensional mediators for linear…
The analysis of natural direct and principal stratum direct effects has a controversial history in statistics and causal inference as these effects are commonly identified with either untestable cross world independence or graphical…
We prove a general theorem showing that local good-$\lambda$ inequalities imply bounds in certain variable Orlicz spaces. We use this to prove results about variable Orlicz Hardy spaces in the unit disc.
We give an elementary introduction, through illustrative examples but without proofs, to one of the basic consequences of the Langlands programme, namely the law governing the primes modulo which a given irreducible integral polynomial…
This paper studies and bounds the effects of approximating loss functions and credal sets on choice functions, under very weak assumptions. In particular, the credal set is assumed to be neither convex nor closed. The main result is that…
We present a rather general version of the snake lemma for abelian groups.
There are a number of measures of direct and indirect effects in the literature. They are suitable in some cases and unsuitable in others. We describe a case where the existing measures are unsuitable and propose new suitable ones. We also…
We prove sharp L^2 boundary decay estimates for the eigenfunctions of certain second order elliptic operators acting in a bounded region, and of their first order space derivatives, using only the Hardy inequality. We then deduce bounds on…
We investigate the first order implicit linear difference equation over residue class rings modulo m. We prove an existence criterion and establish the amount of solutions for this equation. We obtain analogous results for the initial…
We prove explicit bounds on the number of lattice points on or near a convex curve in terms of geometric invariants such as length, curvature, and affine arclength. In several of our results we obtain the best possible constants. Our…