The comprehension of universal thermodynamic behaviors in the supercritical region is crucial for examining the characteristics of black hole systems under high temperature and pressure.This study is devoted to the an...The comprehension of universal thermodynamic behaviors in the supercritical region is crucial for examining the characteristics of black hole systems under high temperature and pressure.This study is devoted to the analysis of characteristic lines and crossover behaviors within the supercritical region.By making use of the free energy,we introduce three key thermodynamic quantities:scaled variance,skewness,and kurtosis.Our results demonstrate that the Widom line,associated with the maximal scaled variance,can effectively differentiate between small and large black hole-like subphases,each displaying distinct thermodynamic behaviors within the supercritical region.Furthermore,by utilizing quasinormal modes,we identify the Frenkel line,offering a dynamic perspective to distinguish between small and large black hole-like subphases.These contribute to a deeper comprehension of black hole subphases in the supercritical region,thus illuminating new facets of black hole thermodynamics.展开更多
The author considers the largest eigenvaiues of random matrices from Gaussian unitary ensemble and Laguerre unitary ensemble, and the rightmost charge in certain random growth models. We obtain some precise asymptotic...The author considers the largest eigenvaiues of random matrices from Gaussian unitary ensemble and Laguerre unitary ensemble, and the rightmost charge in certain random growth models. We obtain some precise asymptotics results, which are in a sense similar to the precise asymptotics for sums of independent random variables in the context of the law of large numbers and complete convergence. Our proofs depend heavily upon the upper and lower tail estimates for random matrices and random growth models. The Tracy-Widom distribution plays a central role as well.展开更多
The paper focuses on the largest eigenvalues of theβ-Hermite ensemble and theβ-Laguerre ensemble. In particular, we obtain the precise moment convergence rates of their largest eigenvalues. The results are motivated...The paper focuses on the largest eigenvalues of theβ-Hermite ensemble and theβ-Laguerre ensemble. In particular, we obtain the precise moment convergence rates of their largest eigenvalues. The results are motivated by the complete convergence for partial sums of i.i.d, random variables, and the proofs depend on the small deviations for largest eigenvalues of the β ensembles and tail inequalities of the generalβ Tracy-Widom law.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12473001,11975072,11875102,11835009,and 11965013)the National SKA Program of China(Grant Nos.2022SKA0110200 and 2022SKA0110203)+1 种基金the National 111 Project(Grant No.B16009)supported by Yunnan High-level Talent Training Support Plan Young&Elite Talents Project(Grant No.YNWR-QNBJ-2018-181).
文摘The comprehension of universal thermodynamic behaviors in the supercritical region is crucial for examining the characteristics of black hole systems under high temperature and pressure.This study is devoted to the analysis of characteristic lines and crossover behaviors within the supercritical region.By making use of the free energy,we introduce three key thermodynamic quantities:scaled variance,skewness,and kurtosis.Our results demonstrate that the Widom line,associated with the maximal scaled variance,can effectively differentiate between small and large black hole-like subphases,each displaying distinct thermodynamic behaviors within the supercritical region.Furthermore,by utilizing quasinormal modes,we identify the Frenkel line,offering a dynamic perspective to distinguish between small and large black hole-like subphases.These contribute to a deeper comprehension of black hole subphases in the supercritical region,thus illuminating new facets of black hole thermodynamics.
基金NSF of China (No.10371109,10671176)the Royal Society K.C.Wong Education Foundation
文摘The author considers the largest eigenvaiues of random matrices from Gaussian unitary ensemble and Laguerre unitary ensemble, and the rightmost charge in certain random growth models. We obtain some precise asymptotics results, which are in a sense similar to the precise asymptotics for sums of independent random variables in the context of the law of large numbers and complete convergence. Our proofs depend heavily upon the upper and lower tail estimates for random matrices and random growth models. The Tracy-Widom distribution plays a central role as well.
基金Supported partly by the National Natural Science Foundation of China (Grant Nos. 11071213, 11101362)Zhejiang Provincial Natural Science Foundation of China (Grant No. R6090034)Research Fund for the Doctoral Program of Higher Education (Grant No. 20100101110001)
文摘The paper focuses on the largest eigenvalues of theβ-Hermite ensemble and theβ-Laguerre ensemble. In particular, we obtain the precise moment convergence rates of their largest eigenvalues. The results are motivated by the complete convergence for partial sums of i.i.d, random variables, and the proofs depend on the small deviations for largest eigenvalues of the β ensembles and tail inequalities of the generalβ Tracy-Widom law.
