arXiv subjects

Ignacio Zalduendo

Publications and source records attributed to Ignacio Zalduendo.

2 recordsLinked to original sources

arXiv2020

Orthant probabilities and the attainment of maxima on a vertex of a simplex

We calculate bounds for orthant probabilities for the equicorrelated multivariate normal distribution and use these bounds to show the following: for degree $k>4$, the probability that a $k$-homogeneous polynomial in $n$ variables attains a relative maximum on a vertex of the $n$-dimensional simplex tends to one as the dimension $n$ grows. The bounds we obtain for the orthant probabilities are tight up to $\log(n)$ factors.

math.PR↗

arXiv2008

Orthogonally additive holomorphic functions of bounded type over $C(K)$

It is known that all $k$-homogeneous orthogonally additive polynomials $P$ over $C(K)$ are of the form $$ P(x)=\int_K x^k dμ. $$ Thus $x\mapsto x^k$ factors all orthogonally additive polynomials through some linear form $μ$. We show that no such linearization is possible without homogeneity. However, we also show that every orthogonally additive holomorphic functions of bounded type $f$ over $C(K)$ is of the form $$ f(x)=\int_K h(x) dμ$$ for some $μ$ and holomorphic $h\colon C(K) \to L^1(μ)$ of bounded type.

math.FA↗