Tootfinder

Central limit theorem and Cram\'{e}r-type moderate deviations for Milstein scheme
Peng Chen, Hui Jiang, Jing Wang
https://arxiv.org/abs/2510.03053 https://

Central limit theorem and Cramér-type moderate deviations for Milstein scheme
In this paper, we investigate the Milstein numerical scheme with step size $η$ for a stochastic differential equation driven by multiplicative Brownian motion. Under some appropriate coefficient conditions, the continuous-time system and its discrete Milstein scheme approximation each possess unique invariant measures, which we denote by $π$ and $π_η$ respectively. We first establish a central limit theorem for the empirical measure $Π_η$, a statistical consistent estimator of $π_η$. Su…

If ICE and DHS continue to mask up to hide their identities then we should presume that *all* people working at ICE/DHS are goons and apply appropriate social measures, such as ostracism, public call-outs, and refusal of service (at stores, restaurants, etc.)

A Noncommutative Szeg\H{o}-Type Theorem on the Row-Ball
Connor J. Gauntlett, David P. Kimsey
https://arxiv.org/abs/2507.19453 https://arxiv.org/pdf/2507.19…

A Noncommutative Szegő-Type Theorem on the Row-Ball
In this paper we leverage the recently developed theory of noncommutative (nc) measures to prove a free noncommutative analogue of many known equalities extending the weak Szegő limit theorem, by applying Constantinescu's theory of Schur parameters to an appropriate kernel on the free monoid on $d$ generators, where $d \geq 1$; in particular, we show that our nc Szegő entropy depends only upon the absolutely continuous part of the associated nc measure. We obtain a correspondence between nc m…

Singular functions obtained via random function iteration
Cristian Mitrea, Alef E. Sterk
https://arxiv.org/abs/2508.16327 https://arxiv.org/pdf/2508.16327

Singular functions obtained via random function iteration
In this paper we consider a discrete-time dynamical system on the real line by random iteration of two functions. These functions are assumed to satisfy appropriate monotonicity conditions; optionally, a symmetry condition may be imposed. Using Bernoulli measures on the space of binary sequences we show that sequences generated by the iteration process almost surely diverge to either plus or minus infinity. The function that assigns to each initial point the probability that the iterates diverg…

Effective regions and kernels in continuous sparse regularisation, with application to sketched mixtures
Yohann De Castro, R\'emi Gribonval, Nicolas Jouvin
https://arxiv.org/abs/2507.08444

Effective regions and kernels in continuous sparse regularisation, with application to sketched mixtures
This paper advances the general theory of continuous sparse regularisation on measures with the Beurling-LASSO (BLASSO). This TV-regularized convex program on the space of measures allows to recover a sparse measure using a noisy observation from an appropriate measurement operator. While previous works have uncovered the central role played by this operator and its associated kernel in order to get estimation error bounds, the latter requires a technical local positive curvature (LPC) assumpti…

Use of a genetic algorithm to find solutions to introductory physics problems
Tom Bensky, Justin Kopcinski
https://arxiv.org/abs/2508.10920 https://arxiv.o…

Use of a genetic algorithm to find solutions to introductory physics problems
In this work, we show how a genetic algorithm (GA) can be used to find step-by-step solutions to introductory physics problems. Our perspective is that the underlying task for this is one of finding a sequence of equations that will lead to the needed answer. Here a GA is used to find an appropriate equation sequence by minimizing a fitness function that measures the difference between the number of unknowns versus knowns in a set of equations. Information about knowns comes from the GA posing …