Tom LaGatta

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Name	Tom LaGatta
Member for	3 years
Seen	2 days ago
Website	cims.nyu.edu/~lagatta
Location	New York City, NY
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I am a postdoc at the Courant Institute at NYU working in probability theory. You may find my pre-prints and publications here on the arXiv.

With Janek Wehr, we have proved a shape theorem for random Riemannian metrics in a general setting. We have also submitted two articles on minimizing geodesics in this random setting. For an introduction to this topic, see the first section of our Geodesics paper.

To control technical estimates for random Riemannian metrics, I have developed some results of continuous disintegrations for Gaussian processes.

I am also interested in political science. With Smith and Bueno de Mesquita, we have developed a general model for voting behavior using game theory. With Andrew Little and Josh Tucker, we have a rational-choice model for the peaceful transfer of power after democratic elections.

stats recent reputation favorites

Apr 19	awarded	● Nice Question
Apr 18	comment	What is a Gaussian measure? Thanks, George. This pretty well answers my question, and at a deeper level of generality than I was asking at originally.
Apr 16	revised	What is a Gaussian measure? added 478 characters in body
Apr 5	awarded	● Popular Question
Mar 24	comment	Riesz representation theorem for vector-valued fields Thanks everybody for your helpful comments.
Mar 24	comment	Generalized Skorokhod spaces Here is a good survey on Skorokhod space and generalizations: kpbc.umk.pl/Content/39953/kievtopologies.pdf
Mar 20	comment	Why can’t there be a general theory of nonlinear PDE? Here is a 7-page review of Partial Differential Relations by Dusa McDuff: projecteuclid.org/DPubS/Repository/1.0/…
Mar 20	answered	Open problems in PDEs, dynamical systems, mathematical physics
Mar 20	comment	Open problems in PDEs, dynamical systems, mathematical physics This is a good question, but should be made Community Wiki. I see that there is already 1 vote to close. To users with closing power: I ask that you keep the question open for at least a few days to collect a few good answers for @AJGibson. If having a big list is annoying at that point, then we can close it.
Mar 18	comment	Riesz representation theorem for vector-valued fields @Willie Wong: I don't know! I usually work with the real- or complex-valued case, in which case $V$ and $V^*$ are isomorphic. Thanks for raising the issue. @jbc: thanks for the reference, that will definitely be a good starting place for me.
Mar 18	revised	Riesz representation theorem for vector-valued fields added 58 characters in body
Mar 18	asked	Riesz representation theorem for vector-valued fields
Mar 15	comment	Extending a Hilbert space isometrically @Jochen Wengenroth: I specifically made no additional assumptions on the Hilbert space nor the larger topological space $X$, such as separability or local convexity. Your remark on the separable case is interesting, and I thank you for making the point. For the second question, I mean to say, "when does F admit the structure of a Fréchet space?" Certainly, if its topology is completely metrizable, then the metric on $F$ will be an extension of the metric from $H$.
Mar 15	revised	Extending a Hilbert space isometrically added 25 characters in body
Mar 15	asked	Extending a Hilbert space isometrically
Mar 14	comment	$C^k$ topology of metrics Here is a reference on Cheeger-Gromov theory: arxiv.org/pdf/gr-qc/0208079v2.pdf
Mar 13	answered	How to triangulate a math reference?
Mar 13	comment	origin of the notion of “network” in graph theory David Aldous defines a network to be "a graph with context-dependent extra structure." stat.berkeley.edu/~aldous/Talks/…
Mar 12	comment	Symmetry group for the frame bundle of a G-space Thank you, @Ryan!
Mar 12	comment	Symmetry group for the frame bundle of a G-space @Ryan Budney, smooth actions are all I am concerned with; I edited the post. Thanks for the quick reply. Could you add a few more details and post that as an answer?
Mar 12	revised	Symmetry group for the frame bundle of a G-space added 9 characters in body
Mar 12	asked	Symmetry group for the frame bundle of a G-space
Mar 11	comment	Gaussian measures on non-separable spaces Indeed, this does answer the question. The Corollary to Theorem 2 states that there is no admissible norm on a non-separable Hilbert space. Since the support of the measure in affine space $X$ is the closure of the Cameron-Martin space corresponding to the covariance operator, the support of the measure must be separable. Consequently, there can be no Gaussian measure with full support in a non-separable affine space. Cheers.
Mar 11	comment	Gaussian measures on non-separable spaces Thanks, @Anatoly Kochubei! Is is the case that in the non-separable setting, Gaussian measures are always concentrated on separable subspaces? It would seem reasonable that the answer is yes, which provides a negative answer to my original question. I was mulling over your second fact last night (the canonical Gaussian cylinder-set measure cannot be extended to a genuine measure), and am glad to see the reference. I'll take a look at Satô's paper and let you know if I've got any questions.
Mar 11	comment	Can random elements be defined in terms of a measure algebra? @Gerald: could you please summarize the image measure catastrophe in a comment?
Mar 11	comment	Gaussian measures on non-separable spaces @Gerald (my apologies for misspelling your name before), a topological affine space is a topological vector space with the origin forgotten. Thankfully, the situation you hypothesize never occurs: there is always the zero functional. In that case, the only centered Gaussian measure is the Dirac point-mass concentrated on the origin.
Mar 10	revised	Gaussian measures on non-separable spaces added 233 characters in body
Mar 10	comment	Gaussian measures on non-separable spaces @Jacob Bell: I suspect that algebraic geometers are the mathematicians who think the most about general categories of spaces like topological affine spaces. I put the tag to get their input.
Mar 10	comment	Gaussian measures on non-separable spaces @Gerald Edgar: good point. We can always construct measures which has support on a finite-dimensional subspace of $X$. Let's add the condition that the support of the measure is the whole space.
Mar 9	asked	Gaussian measures on non-separable spaces
Mar 5	asked	The limiting behavior of geometric random walk
Mar 5	comment	What is a Gaussian measure? Thank you for the nice references, @Liviu Nicolaescu.
Mar 4	awarded	● Nice Question
Mar 3	asked	What is a Gaussian measure?
Feb 28	comment	Why do we choose the standard total order on the integers? Thank you, @Boris Novikov. This is an excellent fact to know.
Feb 28	comment	Why do we choose the standard total order on the integers? Thank you, @quid. This is a great answer to my question.
Feb 28	comment	Why do we choose the standard total order on the integers? Thank you, @Andreas Blass. In a sense, I should have anticipated this answer: if we insist on a total order, then it is not at all surprising that the standard order is the only one.
Feb 28	comment	Why do we choose the standard total order on the integers? @Ryan Budney, one mathematician's pedantry is another's research program. Thank you for sharing your observation on the Sharkovski order; it looks interesting.
Feb 27	asked	Why do we choose the standard total order on the integers?
Feb 27	asked	Is every bornological space measurable?
Feb 26	comment	Probability theory over noncommutative ring? @darij grinberg: can you share a perspective on entropy from the point of view of non-associative algebra? I'd love to hear more about its strangeness.
Feb 21	comment	What is quantum Brownian motion? @Abdelmalek Abdesselam: to clarify, while the review has nothing do with a non-commutative probabilistic description of quantum Brownian motion, I think that non-comm. prob. theory might be one framework in which to precisely describe QBM. I make no claims that this approach is necessary but it may be useful.
Feb 21	comment	What is quantum Brownian motion? Good point, @Uwe Franz. I just found another MathOverflow question on the quantum Wiener process: mathoverflow.net/questions/15973/…
Feb 21	asked	What is quantum Brownian motion?
Feb 20	answered	Math Annotate Platform?
Feb 15	comment	What is a good example of a hyperspace where the base space is non-Hausdorff? @quid & @François: you both have enough reputation, so please feel free to edit the post to change the tags.
Feb 14	revised	What is a good example of a hyperspace where the base space is non-Hausdorff? edited tags
Feb 14	asked	What is a good example of a hyperspace where the base space is non-Hausdorff?
Feb 13	comment	Does every commutative monoid admit a translation-invariant measure? @Benjamin Steinberg: I am not familiar with the concept of minimal ideas in semigroups. What are those? Why are they obstructions to the existence of invariant measures?
Feb 13	comment	Does every commutative monoid admit a translation-invariant measure? That's odd that someone would downvote this. It's a great counterexample, and your argument is elegant. It's going to take me some time to reformulate my question so as to circumvent such obstructions. Thanks very much, @Benjamin Steinberg.

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