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Contact process on interchange process
M. Hil\'ario, D. Ungaretti, D. Valesin, M. E. Vares
https://arxiv.org/abs/2509.02747 https://arxiv.org/pdf/2509.…

Contact process on interchange process
We introduce a model of epidemics among moving particles on any locally finite graph. At any time, each vertex is empty, occupied by a healthy particle, or occupied by an infected particle. Infected particles recover at rate $1$ and transmit the infection to healthy particles at neighboring vertices at rate $λ$. In addition, particles perform an interchange process with rate $\mathsf{v}$, that is, the states of adjacent vertices are swapped independently at rate $\mathsf{v}$, allowing the infe…

Forcing Axioms and construction schemes
Jorge Antonio Cruz Chapital, Osvaldo Guzman, Stevo Todorcevic
https://arxiv.org/abs/2509.01712 https://arxiv.org/pd…

Forcing Axioms and construction schemes
We continue the development of the theory of construction schemes over $ω_1$ as introduced by the third author by studying their relation with forcing axioms. Formally, we introduce the cardinals $\mathfrak{m}^n_{\mathcal{F}}$ and use the consistency of $\mathfrak{m}^2_\mathcal{F}>ω_1$ to prove a fundamental result relating gaps and almost disjoint families over $ω$. The cardinals $\mathfrak{m}_\mathcal{F}$ are also used to prove some limiting results for contstruction schemes, some of which…

$(d,\sigma)$-twisted Affine-Virasoro superalgebras
Rencai L\"u, Xizhou You, Kaiming Zhao
https://arxiv.org/abs/2507.00349 https://

$(d,σ)$-twisted Affine-Virasoro superalgebras
For any finite dimensional Lie superalgebra $\dot{\mathfrak{g}}$ (maybe a Lie algebra) with an even derivation $d$ and a finite order automorphism $σ$ that commutes with $d$, we introduce the $(d,σ)$-twisted Affine-Virasoro superalgebra $\mathfrak{L}=\mathfrak{L}(\dot{\mathfrak{g}},d,σ)$ and determine its universal central extension $\hat{\mathfrak{L}}=\hat{\mathfrak{L}}(\dot{\mathfrak{g}},d,σ)$. This is a huge class of infinite-dimensional Lie superalgebras. Such Lie superalgebras consist …

Stable deformed $\mathfrak{gl}_N$ homology of torus knots
William Ballinger, Eugene Gorsky, Matthew Hogancamp, Joshua Wang
https://arxiv.org/abs/2507.00175

Stable deformed $\mathfrak{gl}_N$ homology of torus knots
We compute the $E_2$ page in the Rasmussen spectral sequence from triply graded to $\mathfrak{gl}_N$ Khovanov--Rozansky stable homology of torus knots. This confirms a weak form of the conjecture of the second author, Oblomkov, and Rasmussen. The main tool is the link-splitting deformation, or $y$-ification, of link homology; in the $y$-ified context, the relevant Rasmussen spectral sequence collapses and we explicitly compute the $y$-ified $\mathfrak{gl}_N$ stable Khovanov--Rozansky homology o…

Optimality of empirical measures as quantizers
March T. Boedihardjo
https://arxiv.org/abs/2508.02615 https://arxiv.org/pdf/2508.02615

Optimality of empirical measures as quantizers
A common way to discretize a probability measure is to use an empirical measure as a discrete approximation. But how far from being optimal is this approximation in the p-Wasserstein distance? In this paper, we study this question in two contexts: (1) optimality among all uniform quantizers and (2) optimality among all (non-uniform) quantizers. In the first context, for p=1, we provide a complete answer to this question up to a polylog(n) factor. From the probabilistic point of view, this resol…

Combinatorics of monoidal actions in Lie-algebraic context
Volodymyr Mazorchuk, Xiaoyu Zhu
https://arxiv.org/abs/2509.01404 https://arxiv.org/pdf/2509.0140…

Combinatorics of monoidal actions in Lie-algebraic context
This paper is, essentially, a survey related to the problem of understanding the combinatorics of the action of the monoidal category of finite dimensional modules over a simple finite dimensional Lie algebra on various categories of Lie algebra modules. A special attention is payed to the Lie algebras $\mathfrak{sl}_2$ and $\mathfrak{sl}_3$. A few new general results are collected at the end.

Mathematical research with GPT-5: a Malliavin-Stein experiment
Charles-Philippe Diez, Luis da Maia, Ivan Nourdin
https://arxiv.org/abs/2509.03065 https://a…

Mathematical research with GPT-5: a Malliavin-Stein experiment
On August 20, 2025, GPT-5 was reported to have solved an open problem in convex optimization. Motivated by this episode, we conducted a controlled experiment in the Malliavin--Stein framework for central limit theorems. Our objective was to assess whether GPT-5 could go beyond known results by extending a \emph{qualitative} fourth-moment theorem to a \emph{quantitative} formulation with explicit convergence rates, both in the Gaussian and in the Poisson settings. To the best of our knowledge, t…

An Improved Lower Bound for the Critical Parameter of the Stavskaya's Process via a Generalized Recurrent Method
Olivier Couronn\'e (MODAL'X)
https://arxiv.org/abs/2507.02452

An Improved Lower Bound for the Critical Parameter of the Stavskaya's Process via a Generalized Recurrent Method
Stavskaya's process, a discrete-time version of the contact process on $\Z$, is known to exhibit a phase transition at a critical parameter $\alpc$ whose exact value remains an open problem. Recent work by Ramos et al. established a lower bound by linking the process's survival to the non-percolation of a dual contour. The probability of this contour was estimated using a recurrent method on a state space of weighted random walks with short-term memory. In this paper, we generalize and extend t…

Oriented bond-site percolation in random environment and contact processes with periodic recovery
Benedikt Jahnel, Lukas L\"uchtrath, Anh Duc Vu
https://arxiv.org/abs/2507.00329

Oriented bond-site percolation in random environment and contact processes with periodic recovery
We investigate oriented bond-site percolation on the planar lattice in which entire columns are stretched. Generalising recent results by Hilário et al., we establish non-trivial percolation under a $(1+\varepsilon)$-th moment condition on the stretches and use this to prove survival of contact processes with periodic recoveries as well as in random environments.