All Questions
3 questions
5
votes
2
answers
245
views
Differentiability of the map $x\mapsto \delta_x$ in the Arens-Eells/Lipschitz-free space
$\DeclareMathOperator\AE{AE}\DeclareMathOperator\Lip{Lip}$Let $\AE(X)$ denote the Arens-Eells space on a Banach space $X$. Consider the map:
$$
\begin{aligned}
\delta: X & \rightarrow \AE(X)
\\
x&...
6
votes
1
answer
261
views
Area of $n$-sphere contained outside $\ell_1$ ball
For a given $r>1$, what is the surface area of $\mathbb S^{n-1}$ (the sphere of radius 1 in $\mathbb R^n$) which is contained outside of the $\ell_1$ ball of radius $r$? Or equivalently, if $X\sim ...
4
votes
1
answer
193
views
A bound on the square distance of a random walk on undirected graph
Fact:
Let $G$ be an $n$-vertex undirected graph and $(X_s)_{s\in \mathbb N}$ a stationary random walk on $G$. Then for every $s\in \mathbb{N}$,
$ \mathbb{E}[d_G(X_s,X_0)^2] \le C s \log n $, for some ...
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