Tootfinder

Critical Point Processes Obtained from a Gaussian Random Field with a View Towards Statistics
Julien Chevallier (SVH, LJK), Jean-Fran\c{c}ois Coeurjolly (LJK, SVH), Rasmus Waagepetersen
https://arxiv.org/abs/2507.04753

Critical Point Processes Obtained from a Gaussian Random Field with a View Towards Statistics
This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical points of latent smooth Gaussian random fields or of subsets of critical points like minima, saddle points etc. Despite of the simplicity of their definition, the mathematical analysis of critical point processes is non-trivial involving for example deep res…

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https://www.bbc.co.uk/programmes/m0022sq7

Covariate adjustment for linear models in estimating treatment effects in randomised clinical trials. Some useful theory to guide simulation
Stephen Senn, Franz K\"onig, Martin Posch
https://arxiv.org/abs/2508.05459

Covariate adjustment for linear models in estimating treatment effects in randomised clinical trials. Some useful theory to guide simulation
Building on key papers that were published in special issues of Biometrics in 1957 and 1982 we propose and develop a three-aspect system for evaluating the effect of fitting covariates in the analysis of designed experiments, in particular randomised clinical trials. The three aspects are: first the effect on residual mean square error, second the effect on the variance inflation factor (VIF) and third the effect on second order precision. We concentrate, in particular, on the VIF and highlight…

IPA: An Information-Preserving Input Projection Framework for Efficient Foundation Model Adaptation
Yuan Yin, Shashanka Venkataramanan, Tuan-Hung Vu, Andrei Bursuc, Matthieu Cord
https://arxiv.org/abs/2509.04398

IPA: An Information-Preserving Input Projection Framework for Efficient Foundation Model Adaptation
Parameter-efficient fine-tuning (PEFT) methods, such as LoRA, reduce adaptation cost by injecting low-rank updates into pretrained weights. However, LoRA's down-projection is randomly initialized and data-agnostic, discarding potentially useful information. Prior analyses show that this projection changes little during training, while the up-projection carries most of the adaptation, making the random input compression a performance bottleneck. We propose IPA, a feature-aware projection framewo…

Gaussian Process Modeling Coronal X-ray Variability of Active Galactic Nuclei
Haiyun Zhang, Dahai Yan, Li Zhang, Niansheng Tang
https://arxiv.org/abs/2507.04715

Gaussian Process Modeling Coronal X-ray Variability of Active Galactic Nuclei
The corona is an integral component of active galactic nuclei (AGNs) which can produce the X-ray emission. However, many of its physical properties and the mechanisms powering this emission remain a mystery. In this work, we study the coronal X-ray variabilities of 13 AGNs by Gaussian Process. 2-10 keV light curves of 13 AGNs can be successfully described by the damped-random walk (DRW) model. The extracted coronal X-ray timescales range from 3 to 50 days. In the plot of variability timescale v…

Randomized Krylov-Schur eigensolver with deflation
Jean-Guillaume de Damas, Laura Grigori
https://arxiv.org/abs/2508.05400 https://arxiv.org/pdf/2508.05400…

Randomized Krylov-Schur eigensolver with deflation
This work introduces a novel algorithm to solve large-scale eigenvalue problems and seek a small set of eigenpairs. The method, called randomized Krylov-Schur (rKS), has a simple implementation and benefits from fast and efficient operations in low-dimensional spaces, such as sketch-orthogonalization processes and stable reordering of Schur factorizations. It also includes a practical deflation technique for converged eigenpairs, enabling the computation of the eigenspace associated with a give…

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Crossings and diffusion in Poisson driven marked random connection models
Alessandra Faggionato, Ivailo Hartarsky
https://arxiv.org/abs/2507.03965 https://…

Crossings and diffusion in Poisson driven marked random connection models
Motivated by applications to stochastic homogenization, we study crossing statistics in random connection models built on marked Poisson point processes on $\mathbb R^d$. Under general assumptions, we show exponential tail bounds for the number of crossings of a box contained in the infinite cluster for supercritical intensity of the point process. This entails the non-degeneracy of the homogenized diffusion matrix arising in random walks, exclusion processes, diffusions and other models on the…

On local large deviations for decoupled random walks
Dariusz Buraczewski, Alexander Iksanov, Alexander Marynych
https://arxiv.org/abs/2508.05178 https://ar…

On local large deviations for decoupled random walks
A decoupled standard random walk is a sequence of independent random variables $(\hat{S}_n)_{n \geq 1}$ such that, for each $n \geq 1$, the distribution of $\hat{S}_n$ is the same as that of $S_n = ξ_1 + \ldots + ξ_n$, where $(ξ_k)_{k \geq 1}$ are independent copies of a nonnegative random variable $ξ$. We consider the counting process $(\hat{N}(t))_{t\geq 0}$ defined as the number of terms $\hat{S}_n$ in the sequence $(\hat{S}_n)_{n \geq 1}$ that lie within the interval $[0, t]$. Under var…

Universality for fluctuations of counting statistics of random normal matrices
J. Marzo, L. D. Molag, J. Ortega-Cerd\`a
https://arxiv.org/abs/2508.04386 https://

Universality for fluctuations of counting statistics of random normal matrices
We consider the fluctuations of the number of eigenvalues of $n\times n$ random normal matrices depending on a potential $Q$ in a given set $A$. These eigenvalues are known to form a determinantal point process, and are known to accumulate on a compact set called the droplet under mild conditions on $Q$. When $A$ is a Borel set strictly inside the droplet, we show that the variance of the number of eigenvalues $N_A^{(n)}$ in $A$ has a limiting behavior given by \begin{align*} \lim_{n\to\infty…