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3 votes
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A variant of the Laplace principle

$\newcommand{\R}{\mathbb R}\newcommand{\eps}{\varepsilon}$In $\R^d$ I am given a sequence of smooth functions $f_\eps(x)$ that converges uniformly to some $f(x)$, which is assumed to be a good rate ...
leo monsaingeon's user avatar
3 votes
0 answers
109 views

Weak convergence of series representing the log characteristic function

Disclaimer. I already asked this question on math.stackexchange.com without any answers or comments as of yet. In which weak sense does the series representation of the log-characteristic function ...
whz's user avatar
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3 votes
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237 views

Reference request: Darboux properties of real-valued set functions (measures, densities, etc.)

Fix a set $S$ and let $f: \mathcal P(S) \rightharpoonup \mathbf R$ be a real-valued partial function on the power set of $S$; denote by $\mathcal D$ the domain of $f$. We say that $f$ has: (i) the ...
Salvo Tringali's user avatar
2 votes
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98 views

Has this "optimal constrained transport" notion of convergence of measures been named and/or studied?

Let $(X,d)$ be a compact metric space, and let $\{\mu_n\}_{n \in \mathbb{N} \cup \{\infty\}}$ be a family of Borel probability measures on $X$. Fix $L \geq 1$. I will say that $\mu_n$ converges in ...
Julian Newman's user avatar
1 vote
0 answers
92 views

Modulus of Continuity, Heat Flow, and Derivative Estimates

Given $f : \mathbf{R}^d \to \mathbf{R}$, define $P_t f$ by \begin{align} (P_t f)(x) = \mathbf{E} \left[ f (x + \sqrt{t} G) \right], \end{align} where $G \sim \mathcal{N} (0, I_d)$ is a standard ...
πr8's user avatar
  • 801
1 vote
0 answers
77 views

Divergence between random variables after transformation

Let $X$ and $Y$ be random variables with laws $\mu_X$, $\mu_Y$ and $d$ be some $f$-divergence (e.g. KL, total variation, Hellinger). Writing $d(X,Y)$ for the divergence between $\mu_X$ and $\mu_Y$, ...
user34500's user avatar
1 vote
0 answers
56 views

Moduli of continuity and Wasserstein differentiability of functions between measures

Let $X=\mathbb{R}^n$; I am also interested in the general case $X$ is a metric space but for simplicity let's focus on Euclidean space. Let $\mathcal{P}(X)$ denote the space of Borel probability ...
JeffHolder's user avatar
1 vote
0 answers
69 views

Norm-averaging reference request

(Apology in advance for the broadness of this question) I recently came across a relatively simple application where I needed to "balance" the "spreaded-out-ness" of a function with the "peaked-ness" ...
charlestoncrabb's user avatar