Tootfinder

Building on the 90s, statistical n-gram language models, trained on vast text collections, became the backbone of NLP research. They fueled advancements in nearly all NLP techniques of the era, laying the groundwork for today's AI.
F. Jelinek (1997), Statistical Methods for Speech Recognition, MIT Press, Cambridge, MA
#NLP

The half-space KPZ line ensemble and its scaling limit
Sayan Das, Christian Serio
https://arxiv.org/abs/2506.07939 https://arxiv.org/…

The half-space KPZ line ensemble and its scaling limit
For each $α\in \mathbb{R}$, $t \geq 1$, we show that there exists a unique $\mathbb{N}$-indexed line ensemble of random continuous curves $\mathbb{R}_{\le 0} \to \mathbb{R}$ with the following properties: (1) The top curve is distributed as the time-$t$ Cole--Hopf solution to the half-space KPZ equation with narrow wedge initial condition and Neumann boundary condition with parameter $α$. (2) The line ensemble satisfies a one-sided resampling invariance property, involving softly non-inte…