Sharp upper tail behavior of line ensembles via the tangent method
U.C. Berkeley（加州大学伯克利分校）；Nanyang Technological University（南洋理工大学）
Shirshendu Ganguly, Milind Hegde
备注：
96 pages, 8 figures. v3: Previously conditional results for the KPZ line ensemble have been made unconditional using arXiv:2512.17823. Abstract suitably modified
We develop a new probabilistic and geometric method to obtain several sharp results pertaining to the upper tail behavior of continuum Gibbs measures on infinite ensembles of random continuous curves, also known as line ensembles, satisfying some natural assumptions. The arguments make crucial use of Brownian resampling invariance properties and correlation inequalities admitted by such Gibbs measures. We obtain sharp one-point upper tail estimates showing that the probability of the value at zero being larger than $θ$ is $\exp(-\frac{4}{3}θ^{3/2}(1+o(1)))$. A key intermediate step is developing a precise understanding of the profile when conditioned on the value at zero equaling $θ$. Our method further allows one to obtain multi-point asymptotics which were out of reach of previous approaches. As an example, we prove sharp explicit two-point upper tail estimates. This framework is then used to establish the corresponding results for the KPZ equation, which are all new. Even for the zero-temperature case of the Airy$_2$ process, our arguments yield new proofs for one-point estimates previously known due to its connections to random matrix theory, as well as new two-point asymptotics. To showcase the reach of the method, we obtain the same results in a purely non-integrable setting under only assumptions of stationarity and extremality in the class of Gibbs measures. Our method bears resemblance to the tangent method introduced by Colomo-Sportiello and mathematically realized by Aggarwal in the context of the six-vertex model.
Sharp asymptotics for $N$-point correlation functions of coalescing heavy-tailed random walk
KLATASDS-MOE, School of Statistics, East China Normal University（华东师范大学统计学院）；NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai（纽约大学上海数学科学研究所）
本文研究了 coalescing 重尾随机游走系统的 N 点相关函数的精确渐进行为，通过尾部估计和非碰撞概率分析，推导了重尾随机游走的精细估计。
Sharp moment estimates for martingales with uniformly bounded square functions
本文给出了平方函数一致有界的鞅的终止分布的指数矩和$p$ -矩$1\leqslant p \leqslant 2$的精确界。我们引入了相应的极值问题的Bellman函数，并将其减少到$\mathrm{BMO}([0,1])$上已知的Bellman函数。在尾部估计的情况下，类似的减少并不完全有效，所以我们提出了一个精细的超解，导致尖尾估计。
The sharp one-dimensional convex sub-Gaussian comparison constant
Department of Statistics and Data Science, The Wharton School, University of Pennsylvania（宾夕法尼亚大学沃顿商学院统计与数据科学系）；School of Mathematics, University of Bristol（布里斯托大学数学学院）
