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@arXiv_mathCO_bot@mastoxiv.page
2025-10-15 10:09:22

Boosted second moment method in random regular graphs
Bal\'azs Gerencs\'er, Viktor Harangi
arxiv.org/abs/2510.12600 arxiv.org/pdf/2…

Boosted second moment method in random regular graphs
Determining the asymptotic independence ratio of random regular graphs is a key challenge in the area of sparse random graphs. Due to the interpolation method, very good upper bounds are known, which are actually known to be sharp for sufficiently large degrees. This paper provides explicit lower bounds for given degrees $d$, beating the previous best bounds for $d \geq 10$. The starting point is a second moment argument that we can boost by arguing that the obtained independent set has a cer…

@njamster@mastodon.gamedev.place
2025-10-14 11:59:59
Content warning: Silksong Patch Notes, Light Spoilers for an Act 3 Boss

"Fixed Crust King Khann sometimes falling out of bounds during entry, when fought on low-end systems" must be the funniest patch note I've read in a while!
Imagine beating all 38 waves of the Coral Tower gauntlet (which, since you're playing on a low-end system, will likely lag and stutter) without finding the shortcut after the third arena, entering the boss arena and then... he just falls out of screen! 🤣

@arXiv_mathAP_bot@mastoxiv.page
2025-10-03 10:07:31

Strichartz and dispersive estimates for quantum bouncing ball model: exponential sums and Van der Corput methods in 1d semi-classical Schr\"odinger equations
Oana Ivanovici (LJLL)
arxiv.org/abs/2510.01779

Strichartz and dispersive estimates for quantum bouncing ball model: exponential sums and Van der Corput methods in 1d semi-classical Schrödinger equations
We analyze the one-dimensional semi-classical Schrödinger equation on the half-line with a linear potential and Dirichlet boundary conditions. Our main focus is on establishing improved dispersive and Strichartz estimates for this model, which govern the space-time behavior of solutions. We prove refined Strichartz bounds using Van der Corput-type derivative tests, beating previous known results where Strichartz estimates incur 1/4 losses. Moreover, assuming sharp bounds for certain exponentia…