Let π be a minimal ErdSs-Szekeres permutation of 1, 2,..., n^2, and let ln,k be the length of the longest increasing subsequence in the segment （πr（1）,...,π（k））. Under uniform measure we establish an exponent...Let π be a minimal ErdSs-Szekeres permutation of 1, 2,..., n^2, and let ln,k be the length of the longest increasing subsequence in the segment （πr（1）,...,π（k））. Under uniform measure we establish an exponentially decaying bound of the upper tail probability for ln,k, and as a consequence we obtain a complete convergence, which is an improvement of Romik＇s recent result. We also give a precise lower exponential tail for ln,k.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
This paper studies the global and local properties of the trajectories of Gaussian random fields with stationary increments and proves sufficient conditions for Strassen's functional laws of the iterated logarithm...This paper studies the global and local properties of the trajectories of Gaussian random fields with stationary increments and proves sufficient conditions for Strassen's functional laws of the iterated logarithm at zero and infinity respectively.The sets of limit points of those Gaussian random fields are obtained.The main results are applied to fractional Riesz-Bessel processes and the sets of limit points of this field are obtained.展开更多
基金Supported by National Natural Science Foundation of China （Grant No. 10671176） and Natural Science Foun- dation of Zhejiang Province （Grant No. J20091364）
文摘Let π be a minimal ErdSs-Szekeres permutation of 1, 2,..., n^2, and let ln,k be the length of the longest increasing subsequence in the segment （πr（1）,...,π（k））. Under uniform measure we establish an exponentially decaying bound of the upper tail probability for ln,k, and as a consequence we obtain a complete convergence, which is an improvement of Romik＇s recent result. We also give a precise lower exponential tail for ln,k.
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 by NSFC(Grants Nos.11671115,11731012 and 11871425)NSF(Grant No.DMS-1855185)
文摘This paper studies the global and local properties of the trajectories of Gaussian random fields with stationary increments and proves sufficient conditions for Strassen's functional laws of the iterated logarithm at zero and infinity respectively.The sets of limit points of those Gaussian random fields are obtained.The main results are applied to fractional Riesz-Bessel processes and the sets of limit points of this field are obtained.
