#probabilitytheory — Public Fediverse posts

#paperOfTheDay is "Correlation functions and zeros of a Gaussian power series and Pfaffians" from 2013.
This paper is a generalisation of the study of random polynomials: They consider random power series, i.e. polynomials with infinitely many terms. These have (almost always) a radius of convergence of unity, so that it only makes sense to study them in the domain (-1,1). There is an accumulation of zeros (=roots) close to the boundaries of this interval.
Given that the coefficients of the power series are random, so are the locations of zeros. The positive locations form an infinite sequence of random numbers, a point process. As such, one can ask about the mean, variance, and all other correlation functions. The main result of the article is that these quantities are given by a Pfaffian (which is an algebraic object similar to a determinant) of some explicitly known matrices.
I got interested in this observation because Pfaffians also show up in #quantumFieldTheory . For example, Isserlis theorem (sometimes called Wicks theorem by physicists) says that the expectation of a product of Gaussian variables is the Pfaffian of their covariances. Or, Pfaffians show up as the integrands in #FeynmanIntegral s in topological field theories.
#mathematics #probabilityTheory
https://projecteuclid.org/journals/electronic-journal-of-probability/volume-18/issue-none/Correlation-functions-for-zeros-of-a-Gaussian-power-series-and/10.1214/EJP.v18-2545.full

2025 is looking like a great year for work at the intersection of #categorytheory, #systemstheory, #controltheory, #machinelearning and #probabilitytheory, this thread will be a very biased collection of works (in no specific order) I'm hoping to read as soon as possible!

Starting with:
"Logical Aspects of Virtual Double Categories"
https://mastoxiv.page/@arXiv_mathCT_bot/113921693949589956

I don't always share #videos of a #dragqueen giving a #tierlist regarding the #films and #games found on #OsamaBinLaden laptop, but when I do, it's Sunday December 29th 2024... I'm not expecting this to happen again. The #ProbabilityTheory be damned.

This #toot brought to you by the #WokeDetector. Say "up yours, you #woke #moralists" to games that try to groom your kids with the trans liberal agenda.

I Ranked Every Movie AND Show On Osama Bin Laden's Hard Drive
https://youtube.com/watch?v=FIM_aG8ZsVA

#FinishedReading #Boole 's Laws of Thought, whose final chapters partly shift attention from #logic to #probabilityTheory and #philosophyOfScience . I don't have a strong sense of his historical standing in either discipline, although for probability there is https://en.m.wikipedia.org/wiki/Boole%27s_inequality . The attraction of probability is clear, with its range of values from 0 to 1, use of '1 -' for negation, multiplication for conjunction (of independent events) etc. There are rhymes here with his logic at least