pierrenyquist.bsky.social
Assoc. prof. in mathematics at Chalmers/University of Gothenburg. Mainly probability, analysis and computational methods, but I like to visit most areas of mathematics. Elected member Young Academy of Sweden. Mostly here for the science, some for the jokes
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Those of us who have to study chaotic systems, aka young children, in that time slot truly appreciate the recordings!
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Jokes on me of course, now that I actually have to write about *checks notes* the role of theorems and proofs in teaching CS students, the concept of proof, proofs in teaching etc...
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the same issues. All in all, this is IMO a nice and technical piece of work, and was part of Adam Lindhe's PhD thesis within the @kawresearch.bsky.social WASP program. There are also plenty of interesting new questions arising from the work, particularly within the ML setting. (9/9)
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working on this, I was visiting @uncchapelhill.bsky.social and Amarjit Budjhiraja, who happened to be working on a similar thing. I thus had the opportunity to pitch some of the ideas to one of the few people who not only knew the underlying material, but was also actively working with some of (8/n)
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"easy" thing to do is to act as if the noise process, which moves much faster, has converged to its equilibrium, and then analyse the state process. This does work, but unsurprisingly gives rise to some tricky approximations that one needs to deal with. On a fortuitous note, while we were (7/n)
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here. So how to handle it? We use what I think is a nice approach based on local ergodicity, which in turn hinges on the fact that because of the decreasing step size you effectively have two different time scales for the state process and the noise process. Once you realise this, the (6/n)
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state-dependent noise. Semi-realted, during the stochastic networks conference in Stockholm last summer Siva Theja Maguluri (GA Tech) was talking about other results for SA, where state-dependent noise was one of the things they could not yet handle. Hopefully there can be som synergy effects (5/n)
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it could be (very) hard to check whether or not the LDP would hold in that case. There are still some assumptions that would be nice to remove—I think it is possible, just technically messy—but we accomplished the main goal. In terms of proving the results, the main challenge comes from the (4/n)
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where the assumption used to establish a large deviation principle was typically the existence of some rather abstract (this is of course a matter of degree) and opaque limit. The point being that unless you were very comfortable with the framework and the specific version of SA of interest (3/n)
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Aside from generalising the previous large deviation results that are out there, and there are only a few, a big aim was to put the assumptions on tangible things, i.e. objects and quantities that are used more or less directly to define the dynamics. This is rather different from past results (2/n)
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On this note, was made aware of this the other day. Just fabulous: www.youtube.com/watch?v=dKJS...
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I did? Good that I am consistent on this! I guess for going deep into martingales there are really a lot of other great books, but as an intro to measure theoretic probability, this one is hard to beat IMO.
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Phrased differently, for every issue back then there would be at least a couple of papers that I would find really interesting and could essentially read with at worst tangential relevance to topics I was working on. Now, instead it seems like there may be a couple of papers over an entire year.
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As an experiment, I went back and looked at issues from a couple of years ~10 years ago. Even though there were of course a big spread in topics back then as well, for most papers I felt that I either had a (vague) grasp of the general topic/problem setting. Not so much now.
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Depends: shift in my own view/feelings, or how I think the journal has changed? For the former, the best way to describe it is probably that it no longer feels like "home". For the latter, a vague way of phrasing it is how much it has moved, IMO, to the "complex analysis-based" part of prob theory.
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"Acknowledged in:" is the first that comes to mind. I like the sound of "non-author contributions", however *I* would interpret that as fairly substantial contributions without being an author, which is not necessarily the same bar as for being acknowledged in a paper.
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If we are being pedantic, it should be Bakry-Émery and Bakry-Gentil-Ledoux; I blame late-night post road trip brain for the omission. Either way, starting to convince myself that this should happen in the not-too-distant future.
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This looks really promising. The intro conjures up the image of a great athlete returning from "retirement" only to dominate the sport/league/... once again.
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Official ad and link to application system is now up. An overall theme of general interest is probability theory and analysis connected to sampling, optimisation and learning in high dimension. Includes, e.g., MCMC, large deviations, optimisation over random structures, stochastic optimisation...
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I know quite a bit of his stuff from way back, but whenever I venture into new areas, I seem to end up reading something he wrote there as well. I generally do not equate what journal you publish in with quality, but I just noticed that he has two papers in Inventiones and c'mon now.
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Well, I prefer not to but have been "forced" to use it in some collaborations. But absolutely, my default is working in a local tex-file, and (of course) to proofread and make corrections on printed versions. So yes, I am of the stone age.
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Nice 📌