On the local limit theorem for general lattice distribution.
On the Markov chain central limit theorem.
On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments
Let be the empirical distribution function (df) pertaining to independent random variables with continuous df . We investigate the minimizing point of the empirical process , where is another df which differs from . If and are locally Hölder-continuous of order at a point our main result states that converges in distribution. The limit variable is the almost sure unique minimizing point of a two-sided time-transformed homogeneous Poisson-process with a drift. The time-transformation...
On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments
Let Fn be the empirical distribution function (df) pertaining to independent random variables with continuous df F. We investigate the minimizing point of the empirical process Fn - F0, where F0 is another df which differs from F. If F and F0 are locally Hölder-continuous of order α at a point τ our main result states that converges in distribution. The limit variable is the almost sure unique minimizing point of a two-sided time-transformed homogeneous Poisson-process with a drift. The time-transformation...
On the moments of sums of independent identically distributed random variables.
On the multiple overlap function of the SK model.
In this note, we prove an asymptotic expansion and a central limit theorem for the multiple overlap R1, ..., s of the SK model, defined for given N, s ≥ 1 by R1, ..., s = N-1Σi≤N σ1i ... σsi. These results are obtained by a careful analysis of the terms appearing in the cavity derivation formula, as well as some graph induction procedures. Our method could hopefully be applied to other spin glasses models.
On the Poisson approximation of the binomial distribution.
On the Poisson approximation to the negative hypergeometric distribution.
On the rate of approximation in the random sum CLT for dependent variables
Capital and lower-case approximations of the expected value of a class of smooth functions of the normalized random partial sums of dependent random variables by the expectation of the corresponding functions of Gaussian random variables are established. The same types of approximation are also obtained for dependent random vectors. This generalizes and improves previous results of the author (1980) and Rychlik and Szynal (1979).
On the rate of convergence in the central limit theorem
On the rate of convergence in the central limit theorem for martingale difference sequences
On the remainder term of the de Moivre-Laplace formula.
On the sphericity of scaling limits of random planar quadrangulations.
On the strong Brillinger-mixing property of -determinantal point processes and some applications
First, we derive a representation formula for all cumulant density functions in terms of the non-negative definite kernel function defining an -determinantal point process (DPP). Assuming absolute integrability of the function , we show that a stationary -DPP with kernel function is “strongly” Brillinger-mixing, implying, among others, that its tail--field is trivial. Second, we use this mixing property to prove rates of normal convergence for shot-noise processes and sketch some applications...
On the tail of the stationary waiting time distribution and limit theorems for the M/G/1 queue
On the traces of Laguerre processes.
On the universal constant in the Katz-Petrov and Osipov inequalities
Upper estimates are presented for the universal constant in the Katz-Petrov and Osipov inequalities which do not exceed 3.1905.
On the Weak Convergence of Stochastic Processes.
On the weak law of large numbers for normed weighted sums of i.i.d. random variables.
On The Zeros Of Oscillatory Solutions Of Linear Second-Order Differential Equations