6,612 reputation
1240
bio website case.edu/artsci/math/mwmeckes
location Toulouse, France
age 36
visits member for 4 years, 6 months
seen 1 hour ago

Assoc. Prof. at CWRU. My main research interests are in probability, geometry, and functional analysis.


Feb
27
answered Hölder's inequality for matrices
Feb
27
awarded  Nice Answer
Feb
19
comment norm of trigonometric polynomials under arbitrary change of signs
@NoahStein: The question is pretty vague as stated, and I assumed "not too small" was an allowable interpretation of "large" (and, for that matter, that "has" can mean "has on average", "has with not too small probability", etc.).
Feb
19
comment norm of trigonometric polynomials under arbitrary change of signs
I'm not sure of the answer to your question off-hand (though I'd guess yes), but the place to start looking for this kind of material is Kahane's book "Some Random Series of Functions".
Feb
12
answered Are there known expressions for total variation distance between $N(0,\sigma_1^2)$ and $N(0,\sigma^2)$
Feb
5
comment Exponential Convexity
@RSG: Yes, you're missing the square in $\zeta^2 h(x)$.
Feb
5
comment Rosenthal like inequality for weak $\mathbb L^p$-norms
Bill: I find it hard to imagine a functional analyst not interested in the $L_p$ spaces, and impossible to imagine a probabilist who is not interested in limit theorems! (Maybe that was really part of your point.) It's worth noting, though, that connections between probability and functional analysis reach well beyond $L_p$ spaces and limit theorems.
Feb
5
comment Exponential Convexity
In any case, something has to be wrong or missing here. In (ii) of the Proposition, $(x_i + x_j)/2$ isn't necessarily in the domain of $h$.
Feb
5
comment Exponential Convexity
Okay, your phrasing is confusing because you refer to "all choices of $\xi_i$… such that" something is true about the $x_i$.
Feb
5
comment Exponential Convexity
What is the relationship between $\xi_i$ and $x_i$?
Feb
5
comment Probability a random Toeplitz matrix is singular
I don't think you'll find this question answered in the literature. You might be interested in this paper:arxiv.org/abs/0902.2472 where I considered a related problem for circulant matrices.
Jan
29
comment How large are the smallest-area projections of a high-dimensional convex body?
Are you sure you have the right expression? The homogeneity looks funny.
Jan
23
comment A generalization of a theorem of Grothendieck
Yes, of course, silly of me to forget that. I guess I got too hung up on the fact that an isometric embedding wasn't strictly needed here. Incidentally, it's worth noting that even though an isometric embedding isn't necessary, it's better than the isomorphic embedding I suggested, for which the norm of the embedding blows up when $p \to \infty$.
Jan
22
comment A generalization of a theorem of Grothendieck
@AliTaghavi: What you need to know is that $L_p$ contains an infinite dimensional Hilbert space, isomorphically. It is not obvious, but it is true and classical. The usual proof is that Khintchine's inequality shows that the span of the Rademacher functions is such a space.
Jan
20
comment Isometric embeddings of metric spaces in Hilbert spaces
@AntonPetrunin: It certainly doesn't help that the title refers to "isometric embeddings of metric spaces", whereas the question is about something rather different from what that phrase usually means.
Jan
8
comment “Smallest” event such that probability greater than a given value
This exact problem is not standard, as far as I know, but it is of similar character to general "isoperimetric-type" problems for probability measures. It certainly makes sense to consider it. It's hard to say much without being more specific about your probability measure, but in general it would probably be more tractable to reformulate the problem as maximizing the probability of a set with given volume.
Jan
4
awarded  Good Answer
Dec
22
comment Generalization of Darboux's Theorem
Yes, I realized that silly mistake and deleted my comment just before you posted your response.
Dec
12
comment Forms of multivariate CLT
@StéphaneLaurent: Sorry! That was a typo both times.
Dec
12
comment Forms of multivariate CLT
@StéphaneLaurent: stats.stackoverflow.com (also known as Cross Validated) is yet another site on the StackExchange network, focusing on statistics. I suppose its existence is advertised wherever StackExchange sites are listed, but I don't personally know where that is.