Upper tail probability estimates of suprema of Gaussian processes by matrices-A number theoretic example

Michel J. G. Weber

Home/Archive/arXiv

arXiv · 2610.26708

Upper tail probability estimates of suprema of Gaussian processes by matrices-A number theoretic example

Michel J. G. Weber

View original source ↗Read source document ↗Export metadata ↓

Abstract

We prove new lower bounds for the upper tail probabilities of suprema of Gaussian processes. We introduce a proper matrix approach. This is continuing recent works of the author on deviations of suprema and decoupling inequalities for parametrized families of Gaussian processes. An application is given to a number theoretic example related to Wintner random Möbius function.

Explore related subjects

math.PR

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Michel J. G. Weber. 2026-10-19. Upper tail probability estimates of suprema of Gaussian processes by matrices-A number theoretic example. https://arxiv.org/abs/2610.26708

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Improved Mixing Rates of Directed Cycles with Additional Sparse Interconnections

We analyze the absolute spectral gap of Markov chains on graphs obtained from a cycle of $n$ vertices and perturbed only at approximately $n^{1/ρ}$ random locations with an appropriate, possibly sparse, interconnection structure. Together with a strong asymmetry along the cycle, the gap of the resulting chain can be bounded inversely proportionally by the longest arc length (up to logarithmic factors) with high probability, providing a significant mixing speedup compared to the reversible version.

math.PR↗

arXiv2026

Strongly vertex-reinforced jump process on graphs with bounded degree

We study asymptotic behaviours of a non-linear vertex-reinforced jump process defined on an arbitrary infinite graph with bounded degree. We prove that if the reinforcement function $w$ is reciprocally integrable and non-decreasing, then the process visits only a finite number of vertices. In the case where $w$ is regularly varying with index $α>1$, we show that the process eventually gets stuck on a star-shaped subgraph and there is exactly one vertex with unbounded local time.

math.PR↗

arXiv2026

A Note on the Stability of Monotone Markov Chains

This note studies monotone Markov chains, a subclass of Markov chains with extensive applications in operations research and economics. While the properties that ensure the global stability of these chains are well studied, their establishment often relies on the fulfillment of a certain splitting condition. We address the challenges of verifying the splitting condition by introducing simple, applicable conditions that ensure global stability. The simplicity of these conditions is demonstrated through various examples including autoregressive processes, portfolio allocation problems and resource allocation dynamics.

math.PR↗