MathOverflow Questions, Problems & Solutions : TransWikia.com ~ Page 35

Groupoids as models of symmetric simplicial sets

In the Elephant, Peter Johnston remarks that internal categories may be regarded as simplicial objects that “preserve all limits that happen to exist in $Delta^{op}$“ (I guess you might...

Asked on 01/09/2021 by Ben MacAdam

1 answer

Real part of a holomorphic section of a vector bundle

Let $Fto M$ be a holomorphic vector bundle over a complex manifold $M$ and let $s:Mto F$ be a no-zero section. Let $E$ be the complexification...

Asked on 01/08/2021 by user158773

0 answer

"Trade-off" between bound on the function and on the spectrum for functional calculus in spectral theory

Let $A$ be a self-adjoint (unbounded) operator on a separable Hilbert space $H$.From the following form of spectral theorem, we may define a functional calculus by ...

Asked on 01/08/2021 by Ma Joad

0 answer

Gaussian expectation of outer product divided by norm (check)

I am trying to get compute at least the directional component of the following expectation, where $M$ is a symmetric, invertible, PD matrix:$$mathbb{E}_{v sim N(0, I)}left[frac{vv^T}{||Mv||_2}right]$$ (Note...

Asked on 01/07/2021 by B Merlot

1 answer

If $W$ is a Markov chain and $N$ is a Poisson process, then $left(W_{N_t}right)_{tge0}$ is Markov

Let $(Omega,mathcal A,operatorname P)$ be a probability space, $(E,mathcal E)$ be a measurable space, $(W_n)_{ninmathbb N_0}$ be a time-homogeneosu Markov chain on $(Omega,mathcal A,operatorname P)$ with...

Asked on 01/07/2021

0 answer

Open problems in matroid theory

I read Oxley's book on matroid theory and found the theory fascinating. At the end, Oxley stated some open problems and conjectures in matroid theory.Are there any modern lists about...

Asked on 01/06/2021 by LogicTheorist

2 answer

Automorphism group of Hermitian symmetric spaces

For a hermitian symmetric space $M$ one has its group of biholomorphic maps $operatorname{Hol}(M)$ and its group of Riemannian isometries $operatorname{Isom}(M)$. According to Prop. 1.6 of ...

Asked on 01/05/2021 by ThiKu

1 answer

Existence of Gaussian random field with prescribed covariance

Suppose a function $G:mathbb{R}^drightarrowmathbb{R}$ is given. What are some necessary or sufficient conditions on $G$ for there to exist a probability space $(Omega,mathcal{F},mathbb{P})$ and a jointly-measurable function...

Asked on 01/05/2021 by Cabbage

1 answer

What, precisely, do we mean when we say that a f.d. vector space is canonically isomorphic to its double dual?

I've been reading the Xena Project blog, which has been loads of fun. In the linked post Kevin gives the natural isomorphism $V to V^{ast ast}$ from...

Asked on 01/04/2021 by Qiaochu Yuan

0 answer

Discrete logarithm for polynomials

Let $p$ be a fixed small prime (I'm particularly interested in $p = 2$), and let $Q, R in mathbb{F}_p[X]$ be polynomials. Consider the problem of determining...

Asked on 01/04/2021 by Adam P. Goucher

1 answer

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