相关论文: Scaling limits for the Lego discrepancy
We study Mandelbrot's percolation process in dimension $d \geq 2$. The process generates random fractal sets by an iterative procedure which starts by dividing the unit cube $[0,1]^d$ in $N^d$ subcubes, and independently retaining or…
A random walk generated by a sum of independent identity distributed random variables with positive expectation is considered. The limiting distributions for the first- passage -time of a step-function boundary are derived.
Let $M_n$ be the minimal position at generation $n$, of a real-valued branching random walk in the boundary case. As $n \to \infty$, $M_n- {3 \over 2} \log n$ is tight (see [1][9][2]). We establish here a law of iterated logarithm for the…
This work will appear as a chapter in a forthcoming volume titled "Topics in Probabilistic Graph Theory". A theory of scaling limits for random graphs has been developed in recent years. This theory gives access to the large-scale geometric…
The use of continuous probability distributions has been widespread in problems with purely discrete nature. In general, such distributions are not appropriate in this scenario. In this paper, we introduce a class of discrete and asymmetric…
We present a general theorem on the structure of bivariate generating functions which gives sufficient conditions such that the limiting probability distribution is a half-normal distribution. If $X$ is a normally distributed random…
The five-dimensional Ising model with free boundary conditions has recently received a renewed interest in a debate concerning the finite-size scaling of the susceptibility near the critical temperature. We provide evidence in favour of the…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
Nonparametric maximum likelihood estimators (MLEs) in inverse problems often have non-normal limit distributions, like Chernoff's distribution. However, if one considers smooth functionals of the model, with corresponding functionals of the…
We introduce a generic class of dynamic nonlinear heterogeneous parameter models that incorporate individual and time fixed effects in both the intercept and slope. These models are subject to the incidental parameter problem, in that the…
We investigate the phase behaviour of random copolymers melts via large scale Monte Carlo simulations. We observe macrophase separation into A and B--rich phases as predicted by mean field theory only for systems with a very large…
We investigate the probability for the largest segment in with total displacement $Q$ in an $N$-step random walk to have length $L$. Using analytical, exact enumeration, and Monte Carlo methods, we reveal the complex structure of the…
Based on differences of generalized R\'enyi entropies nontrivial constraints on the shape of the distribution function of broadly distributed observables are derived introducing a new parameter in order to quantify the deviation from…
The ``Brownian bees'' model describes an ensemble of $N=$~const independent branching Brownian particles. The conservation of $N$ is provided by a modified branching process. When a particle branches into two particles, the particle which…
Recent empirical work has shown that human children are adept at learning and reasoning with probabilities. Here, we model a recent experiment investigating the development of school-age children's non-symbolic probability reasoning ability…
The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation…
The distribution of masses of clusters smaller than the infinite cluster is evaluated at the percolation threshold. The clusters are ranked according to their masses and the distribution $P(M/L^D,r)$ of the scaled masses M for any rank r…
Sufficient conditions are provided under which the log-likelihood ratio test statistic fails to have a limiting chi-squared distribution under the null hypothesis when testing between one and two components under a general two-component…
In particle-in-cell simulations and some other statistical computations, the representation of modelled distributions with tracked macro-particles can become locally excessive. Merging or resampling dense clusters or highly-populated phase…
Logistic models are studied as a tool to convert output from numerical weather forecasting systems (deterministic and ensemble) into probability forecasts for binary events. A logistic model obtains by putting the logarithmic odds ratio…