On the universality of fluctuations for the cover time
Universität Wien（维也纳大学）；University of British Columbia（不列颠哥伦比亚大学）；Université de Lorraine（洛林大学）
Nathanaël Berestycki, Jonathan Hermon, Lucas Teyssier
备注：
v4:57 pages. Version revised following reviewer's comments. In particular, the improvement of the Aldous-Brown estimates on the exponential approximation for hitting times of sets have been separated from this article and can instead be found in arXiv:2601.03864. Section 3 in particular has also been restructured
We consider random walks on finite vertex-transitive graphs $Γ$ of bounded degree. We find a simple geometric condition which characterises the cover time fluctuations: the suitably normalised cover time converges to a standard Gumbel variable if and only if $\mathrm{Diam}(Γ)^2 = o(n/\log n)$, where $n = |Γ|$. We prove that this condition is furthermore equivalent to the decorrelation of the uncovered set. The arguments rely on recent breakthroughs by Tessera and Tointon on finitary versions of Gromov's theorem on groups of polynomial growth, which we leverage into strong heat kernel bounds, and refined quantitative estimates on Aldous and Brown's exponential approximation of hitting times, which are of independent interest.
Correlation functions for random complex zeroes: strong clustering and local universality
证明了高斯整函数零点的k点关联函数的强聚类性。在证明过程中，我们还得到了任意非退化高斯解析函数零点的k点函数的泛局部界。在本文的第二部分中，我们证明了强聚类产生的高斯整函数的零点的一些线性统计量的波动的渐近正态性，特别是，在可测量的大区域的零点的数量。这补充了我们最近在论文“Fluctuations in random complex zeroes”（arXiv：1003.4251v1）中的结果。
A universality property for large deviations of RWRE close to the axis
Fac. Cs. Exactas y Naturales, Universidad de Buenos Aires and IMAS UBA-CONICET（布宜诺斯艾利斯大学理学院与自然科学系及IMAS UBA-CONICET）；NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai（纽约大学上海校区纽约-华东师范大学数学科学研究所）；Facultad de Matemáticas, Pontificia Universidad Católica de Chile（智利天主教公立大学数学学院）
A universality property for last-passage percolation paths close to the axis
在$Z_+^2$中考虑最后一次通过定向渗流模型，其中i.i.d.其公共分布具有有限$(2+p)$阶矩的权重。我们研究了从原点到点$\big(n,n^{\lfloor a \rfloor}\big)$的通过时间的涨落。我们发现，对于合适的$a$（取决于$p$），这个数量，适当缩放，收敛分布为$n\to\infty$的Tracy-Widom分布，无论潜在的权重分布。该论点使用耦合到布朗定向渗流问题和Komlós，Major和Tusnády的强近似。
