I don't want to give away too much due to anonymity reasons, but the problems are generally in the following areas (in order from hardest to easiest):

- One problem on using quantum mechanics and C*-algebra techniques for non-Markovian stochastic processes. The interchange between the physics and probability languages often trips the models up, so pretty much everything tends to fail here.

- Three problems in random matrix theory and free probability; these require strong combinatorial skills and a good understanding of novel definitions, requiring multiple papers for context.

- One problem in saddle-point approximation; I've just recently put together a manuscript for this one with a masters student, so it isn't trivial either, but does not require as much insight.

- One problem pertaining to bounds on integral probability metrics for time-series modelling.

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MinimalAction 2 days ago | parent | next [-]

Regarding the first problem: are you looking at NCP maps for non-Markovian processes given you mention C*-algebra? Or is it more of a continuous weak monitoring of a stochastic system that results in dynamics with memory effects?

I'd be very curious to know how any LLMs fare. I completely understand if you don't want to continue the discussion because of anonymity reasons.

	▲	hodgehog11 2 days ago \| parent [-]
		More of the latter. It's a pet project of mine, and all of the LLMs tend to utterly fail at getting anywhere with it, at least in chats. In an agentic setup, it can chip away at some aspects, but it needs serious guidance on relevant language, notation, and concepts. To me, it demonstrates that the LLMs are not particularly good at crossing literatures, but then again, humans rarely seem to be good at that either...

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pm2r 2 days ago | parent | prev [-]

It would be wonderful to have a deeper insight, but I understand that you can disclose your identity (I understand that you work in applied research field, right ? )

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hodgehog11 2 days ago | parent [-]

Yes, I do mostly applied work, but I come from a background in pure probability so I sometimes dabble in the fundamental stuff when the mood strikes.

Happy to try to answer more specific questions if anyone has any, but yes, these are among my active research projects so there's only so much I can say.

	▲	pm2r 2 days ago \| parent [-]
		Thanks a lot for your kind but detailed answer. I’m no more in the research field but you gave me good ideas to work on