Inference in quantum physics

In quantum physics all experimental information is discrete and stochastic. But the values of physical quantities are considered to depict definite properties of the physical world. Thus physical quantities should be identified with mathematical variables which are derived from the experimental data, but which exhibit as little randomness as possible. We look for such variables in two examples by investigating how it is possible to arrive at a value of a physical quantity from intrinsically stochastic data. With the aid of standard probability calculus and elementary information theory, we are necessarily led to the quantum theoretical phases and state vectors as the first candidates for physical quantities.     

On a relationship between Uspensky's theorem and poisson approximations

In this paper we show that Uspensky's expansion theorem for the Poisson approximation of the distribution of sums of independent Bernoulli random variables can be rewritten in terms of the Poisson convolution semigroup. This gives rise to exact evaluations and simple remainder term estimations for the deviations of the distributions in study with respect to various probability metrics, generalizing results of Shorgin (1977, Theory Probab. Appl., 22, 846–850). Finally, we compare the sharpness of Poisson versus normal approximations.     

不同类型随机变量和差积商的分布

研究两种不同类型的随机变量,即离散型随机变量ζ与连续型随机变量η的和（ζ＋η）、差（ζ-η）、积（ζη）、商（ζ/η）的分布,给出这些分布的密度函数．     

Gaussian,non-Gaussian critical fluctuations in the Curie-Weiss model

It is known that at the critical temperature the Curie-Weiss mean-field model has non-Gaussian fluctuations and that internal fluctuations can be Gaussian. Here we compute the distribution of theq-mode magnetization fluctuations as a function of the temperature, the wave vectorq, and a fading out external field. We obtain new classes of probability distributions generated by this external field as well as new critical behavior in terms of its rate of fading out. We discuss also the susceptibility as the limitq tending to zero.     

BaFClxBr1－x:Sm2+中5D2→7F0跃迁几率及其对烧孔效率的影响

本文以BaFClxBr1－x:Sm2+中5D2→7F0的跃迁几率随x变化为中心对BaFClxBr1－x:Sm2+体系4f5d带的激发光谱、5D2→7F0跃迁的荧光衰减随温度的变化特性、5D2→7F0的跃迁几率等进行了研究。从而得出结论:在BaFClxBr1－x:Sm2+中,随Br含量的增大,4f5d带与5D2能级更加接近,使7F0→5D2的吸收截面增大,从而可能提高在5D2:能级烧孔的效率。     

里德伯Cs原子与CCl4分子的碰撞电离研究

为描述里德伯Ｃｓ原子与ＣＣｌ４分子碰撞电离实验研究中所发现的若干特征,对里德伯原子与分子碰撞的理论模型－准自由电子模型提出两点修正：（１）考虑原子实在碰撞过程中的作用,并且计入量子亏损;（２）考虑碰撞后正负离子的分离几率。利用修正的模型进行了理论计算,得到了与实验测量较为吻合的结果,。同时与其它文献结果进行了比较。     

条件期望与三变量独立性的两个充要条件

随机事件的独立性、随机变量的独立性是概率统计中的重要概念,不少学者都在这方面有所讨论.本文作者讨论了三维连续型随机变量（X,Y,Z）中三个分量X,Y,Z的相互独立性、条件独立性,得到三个引理.利用条件期望及三个引理作者给出了三变量相互独立的两个充要条件.     

带启动时间的N-策略Geo/G/1排队系统的队长分布及容量的优化设计

考虑带启动时间的N-策略离散时间Geo/G/1排队系统,使用全概率分解技术,从任意初始状态出发,研究了队长的瞬态和稳态性质,推导出了在任意时刻n瞬态队长分布的z -变换的递推表达式、稳态队长分布的递推表达式和附加队长分布的表达式,并获得稳态队长的随机分解结果.最后,通过数值实例,讨论了稳态队长分布对系统参数的敏感性,并阐述了获得便于计算的稳态队长分布的表达式在系统容量的优化设计中的重要应用价值.     

随机矩阵乘积的尾概率

在一定条件下,本文给出了一列正随机矩阵乘积的尾概率估计,它以指数的速度消失;然后,在一维的情形,基于更新过程的残差等待时间的拉普拉斯变换,建立了极限常数的两种不同形式表达式之间的联系.     

Precise asymptotics in the deviation probability series of self-normalized sums

Let X,X₁,X₂,… be a sequence of nondegenerate i.i.d. random variables with zero means. Set Sn=X₁+?+Xn and . In the present paper we examine the precise asymptotic behavior for the general deviation probabilities of self-normalized sums, Sn/Wn. For positive functions g(x), ?(x), α(x) and κ(x), we obtain the precise asymptotics for the following deviation probabilities of self-normalized sums: