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Q&A for professional mathematicians
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Hottest Questions Today - MathOverflow
Skip to main content Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, ...
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I hope everyone is doing well. Let $K \subset \mathbb{R}^n$ be a centrally symmetric convex body $(K = -K)$. Denote by $K \mid H$ the orthogonal projection of $K$ onto $H$, where $H$ is an $n - 1$
Mathoverflow.net news digest
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5 years
Question/References on the Skorokhod M1 topology
Let $D(0,T)$ be the space of right continuous functions with left limits defined on $[0,T]$. Consider the Skorokhod M1 topology on $D(0,T)$, see e.g. S. Ledger, Skorokhod’s M1 topology for distribution-valued processes (ProjectEuclid link DOI)for its...
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14 days
Is there an "equationally presented" version of Cayley's theorem for abelian gro...
Given a set $A$ and a variety (in the sense of universal algebra) $\mathbb{V}$, let $\mathbb{V}(A)$ be the set of all $\mathbb{V}$-algebras with underlying set $A$. Let $\mathbb{G}$ be the variety of groups. Given a group $G$, I'll write "$\underline...
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0 days
When are "hypercube-definable" sets definable hypercubes?
Say that a class of structures $\mathbb{K}$ (all of the same similarity type) is product-nice iff, whenever $\mathcal{M}_1,...,\mathcal{M}_n\in\mathbb{K}$ and $\varphi(\overline{x})$ is a formula in the language of $\mathbb{K}$, the relation $\prod ...
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0 days
How far can the geometric median be from the mean under variance normalization?
Let $X$ be a random variable in $\mathbb{R}^d$ with law $\mu$. We denote by $\mathcal{P}(\mathbb{R}^d)$ the set of all Borel probability measures on $\mathbb{R}^d$.
Assume that $\mu \in \mathcal{P}(\mathbb{R}^d)$ has finite second moment. Its mean is$$\bar{\mu} = \mathbb{E}_\mu[X],$$and its variance is$$\sigma^2(\mu) = \mathbb{E}_\mu\big[\|X - \mathbb{E}_\mu[X]\|^2\big].$$...
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