Markov Processes

对于一般类型的随机矩阵的大小为$n$有独立的项目，典型的特征值的顺序为$\sqrt n$。我们已经研究了大偏差性质时，我们正在寻找的特征值是$n$。 我们已经研究过尾部衰减速度比高斯衰减速度快的情况，现在我们打算研究高斯情况，我们预计结果会有所不同。大偏差理论处理稀有事件概率的估计。它们必然是微小的，并且在某些自然参数中通常是指数小的。该理论处理的是以一定的精度估计指数速率。当我们研究随机变量的总和时，这通常涉及到对总和的指数矩的期望的估计。我们已经建议在某些不寻常但一般的形式，有其他情况下的应用程序的总和来检查这种现象。

For a general class of random matrices of size $n$ having independent entries, the typical eigenvalue is of order $\sqrt n$. We had investigated the large deviation properties when we are looking for eigenvalues that are of order $n$. We had looked at the case when the tails decay faster than Gaussian and now plan to examine the Gaussian case and we expect the results to be somewhat different.Large deviation theory deals with the estimation of probabilities of rare events. They are necessarily tiny and are often exponentially small in some natural parameter. The theory deals with estimating with some precision the exponential rate. When we study sums of random variables this often involves the estimation of the expectation of exponential moments of the sums. We have proposed to examine this phenomena in certain sums of unusual but general form that have applications to other contexts.