Tootfinder

Ballistic aggregation displays self-organized criticality
Krzysztof Burdzy
https://arxiv.org/abs/2508.08613 https://arxiv.org/pdf/2508.08613

Ballistic aggregation displays self-organized criticality
Consider the convex hull of a collection of disjoint open discs with radii $1/2$. The boundary of the convex hull consists of a finite number of line segments and arcs. Randomly choose a point in one of the arcs in the boundary so that the density of its distribution is proportional to the arc measure. Attach a new disc at the chosen point so that it is outside of the convex hull and tangential to its boundary. Replace the original convex hull with the convex hull of all preexisting discs and t…

Samesies.
As I was with the Metaverse. As I will have been with "AI".
It's as if there was a pattern of people with domain experience valuing good solutions who call out bullshit tend to be right.
https://mastodon.social/@mhoye/115174150692070811

Chevalley property and discriminant ideals of Cayley-Hamilton Hopf Algebras
Yimin Huang, Zhongkai Mi, Tiancheng Qi, Quanshui Wu
https://arxiv.org/abs/2506.21879

Chevalley property and discriminant ideals of Cayley-Hamilton Hopf Algebras
For any affine Hopf algebra $H$ which admits a large central Hopf subalgebra, $H$ can be endowed with a Cayley-Hamilton Hopf algebra structure in the sense of De Concini-Procesi-Reshetikhin-Rosso. The category of finite-dimensional modules over any fiber algebra of $H$ is proved to be an indecomposable exact module category over the tensor category of finite-dimensional modules over the identity fiber algebra $H/\mathfrak{m}_{\overline{\varepsilon}}H$ of $H$. For any affine Cayley-Hamilton Hopf…

Remarks on Associated Varieties and Minimal Tension Holography
Andrea E. V. Ferrari
https://arxiv.org/abs/2507.13223 https://arxiv.or…

Remarks on Associated Varieties and Minimal Tension Holography
We comment on certain analogies that have recently emerged between path integral localisation phenomena in minimal tension string theory on $\mathrm{AdS}_3\times S^3\times T^4$ and associated varieties of boundary vertex algebras of 3d $\mathcal{N}=4$ theories. We give evidence for the fact that the path integral localisation relies on an intriguing relation between the conformal boundary of $\mathrm{AdS}_3$ and the associated variety of $V_1(\mathfrak{psl}(2|2))$, (the complexification of…

Gorenstein Normal tangent cones of integrally closed ideals in two-dimensional normal singularities
Tomohiro Okuma, Kei-ichi Watanabe, Ken-ichi Yoshida
https://arxiv.org/abs/2508.17642

Gorenstein Normal tangent cones of integrally closed ideals in two-dimensional normal singularities
Let $(A,\mathfrak m)$ be a two-dimensional excellent normal Gorenstein local domain containing an algebraically closed filed. Let $I =H^0(X,\mathcal{O}_X(-Z)) \subset A$ be an $\mathfrak m$-primary integrally closed ideal represented by an anti-nef cycle $Z$ on some resolution $X\to \mathrm{Spec} A$. In this paper, we prove that $\overline{G}(I)$ is Gorenstein if and only if it is Cohen-Macaulay and $(r-1)Z^2+K_XZ=0$, where $r=\bar{\athrm{r}}(I)$ denotes the normal reduction number of $I$ and $…

Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scaling
Lucas Benigni, Elliot Paquette
https://arxiv.org/abs/2508.20036 https://arxiv…

Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scaling
We compute the asymptotic eigenvalue distribution of the neural tangent kernel of a two-layer neural network under a specific scaling of dimension. Namely, if $X\in\mathbb{R}^{n\times d}$ is an i.i.d random matrix, $W\in\mathbb{R}^{d\times p}$ is an i.i.d $\mathcal{N}(0,1)$ matrix and $D\in\mathbb{R}^{p\times p}$ is a diagonal matrix with i.i.d bounded entries, we consider the matrix \[ \mathrm{NTK} = \frac{1}{d}XX^\top \odot \frac{1}{p} σ'\left( \frac{1}{\sqrt{d}}XW \right)D…

The exact recovery with sub-exponential measurement matrix
Dai Guozheng Diao Tiankun
https://arxiv.org/abs/2506.17965 https://arxiv.o…

The exact recovery with sub-exponential measurement matrix
Let $A$ be an $m \times n$ random matrix, where each entry is an i.i.d.sub-exponential random variable with mean 0 and variance $\frac{1}{m^2}$. We demonstrate that, with high probability, the sub-exponential matrix $A$ can be used for the exact reconstruction of $s$-sparse vectors via $\ell_1$-minimization, provided that $m \ge C_1 s \log\left(\frac{C_2 n}{s}\right)$. This improves upon the existing results by Adamczak et al.