Tootfinder

On the entropy growth of sums of iid discrete random variables
Riccardo Castellano, Pavel Sekatski
https://arxiv.org/abs/2508.05348 https://arxiv.org/pdf/2…

On the entropy growth of sums of iid discrete random variables
We derive an asymptotic lower bound on the Shannon entropy $H$ of sums of $N$ arbitrary iid discrete random variables. The derived bound $H \geq \frac{r(X)}{2}\log(N) + {\it cst}$ is given in terms of the incommensurability rank $r(X)$ of the random variable -- a positive integer quantity that we introduce. The derivation does not rely on central limit theorems, but builds upon the known expressions of the asymptotic entropy of the multinomial distribution and sums of iid lattice random variabl…

Constructing new probability distributions on the unit interval
Roberto Vila, Helton Saulo, Poliana Matos, Subhankar Dutta
https://arxiv.org/abs/2508.01154 https://

Constructing new probability distributions on the unit interval
In this paper, we introduce a novel method for constructing probability distributions on the unit interval by exploiting the non-injective transformation defined by the ratio of two positive random variables, $X$ and $Y$. For simplicity and tractability, we focus on independent random variables $X$ and $Y$ following gamma distributions. We derive some results including laws, density functions, quantile function and closed-form expressions for the moments, and discuss maximum likelihood estimati…

from my link log —
A catalog of ways that compilers generate SSA.
https://bernsteinbear.com/blog/ssa/
saved 2025-02-11 https://

Rebound: Efficient, Expressive, and Well-Scoped Binding
No\'e De Santo, Stephanie Weirich
https://arxiv.org/abs/2509.13261 https://arxiv.org/pdf/2509.1…

Rebound: Efficient, Expressive, and Well-Scoped Binding
We introduce the Rebound library that supports well-scoped term representations in Haskell and automates the definition of substitution, alpha-equivalence, and other operations that work with binding structures. The key idea of our design is the use of first-class environments that map variables to expressions in some new scope. By statically tracking scopes, users of this library gain confidence that they have correctly maintained the subtle invariants that stem from using de Bruijn indices. B…

Covariance as a commutator
Carlos Garc\'ia Meixide
https://arxiv.org/abs/2508.09102 https://arxiv.org/pdf/2508.09102

Covariance as a commutator
The covariance between real finite variance random variables can be expressed as the commutator of taking expectations and multiplying, both viewed as operators extended to act jointly on pairs of functions. The efficient influence curve of the mean represents a centering operator which we demonstrate to interact with expectations and products through simple commutator identities. These expressions reveal an underlying Lie algebraic structure that endows the calculus of efficient influence curv…