Tootfinder

I do not seek the ignorant; the ignorant seek me -- I will instruct them.
I ask nothing but sincerity. If they come out of habit, they become tiresome.
-- I Ching

Matrix Random Walks and the Lima Bean Law
Bruce K. Driver, Brian C. Hall, Ching Wei Ho, Todd Kemp, Yuriy Nemish, Evangelos A. Nikitopoulos, Felix Parraud
https://arxiv.org/abs/2510.10712

Matrix Random Walks and the Lima Bean Law
A matrix random walk is a stochastic process of the form $B_k = (I+A_1)\cdots(I+A_k)$ where $A_j$ are independent ``step'' matrices in $\mathrm{M}_N(\mathbb{C})$. With the right entry-covariance, a rescaled matrix random walk converges to Brownian motion $B(t)$ on a matrix Lie group. In this paper, we study the eigenvalues of such rescaled matrix random walks, as $N\to\infty$ and $k\to\infty$. The standard Brownian motion $W(t)$ on $\mathrm{M}_N(\mathbb{C})$ has independent Gaussian entries a…

Characterizing Temperatures of Flares on the M Dwarf Wolf 359 from Simultaneous Multiband Optical Observations
Chia-Lung Lin, Li-Ching Huang, Wei-Jie Hou, Hsiang-Yao Hsiao, Wing-Huen Ip
https://arxiv.org/abs/2509.21505

Characterizing Temperatures of Flares on the M Dwarf Wolf 359 from Simultaneous Multiband Optical Observations
We present a flare temperature study of the highly active M~dwarf Wolf~359 using simultaneous multiband ($u$, $g$, $r$, $i$, and $z$) photometric observations from the Lulin 1-m and 41-cm telescopes. Twelve flares were detected over five nights, with significant brightness increases in the $u$, $g$, and $r$~bands; only three were seen in $i$, and none in $z$. From broadband SED fitting and $g$/$r$ color ratio, we derive an average flare temperature of $5500 \pm 1600$~K, significantly cooler tha…