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Test for submodel in Gibbs-Markov binary random sequence
Testing a homogeneity of stochastic processes
The paper concentrates on modeling the data that can be described by a homogeneous or non-homogeneous Poisson process. The goal is to decide whether the intensity of the process is constant or not. In technical practice, e.g., it means to decide whether the reliability of the system remains the same or if it is improving or deteriorating. We assume two situations. First, when only the counts of events are known and, second, when the times between the events are available. Several statistical tests...
The Aizenman-Sims-Starr and Guerra's schemes for the SK model with multidimensional spins.
The Arcsine law as the limit of the internal DLA cluster generated by Sinai’s walk
We identify the limit of the internal DLA cluster generated by Sinai’s walk as the law of a functional of a brownian motion which turns out to be a new interpretation of the Arcsine law.
The asymmetric simple exclusion model with multiple shocks
The atomic and molecular nature of matter.
The purpose of this article is to show that electrons and protons, interacting by Coulomb forces and governed by quantum statistical mechanics at suitable temperature and density, form a gas of Hydrogen atoms or molecules.
The best bounds in a theorem of Russell Lyons.
The Bethe lattice spin glass at zero temperature
The branching process in a brownian excursion
The busy period of a repairman attending a unit parallel system
The busy period of a repairman for redundant repairable systems
The center of mass of the ISE and the Wiener index of trees.
The classical limit of a class of quantum dynamical semigroups
The classical limit of reduced quantum stochastic evolutions
The cluster size distribution for a forest-fire process on .
The continuum reaction-diffusion limit of a stochastic cellular growth model
A competition-diffusion system, where populations of healthy and malignant cells compete and move on a neutral matrix, is analyzed. A coupled system of degenerate nonlinear parabolic equations is derived through a scaling procedure from the microscopic, Markovian dynamics. The healthy cells move much slower than the malignant ones, such that no diffusion for their density survives in the limit. The malignant cells may locally accumulate, while for the healthy ones an exclusion rule is considered....
The dam with content-dependent input and output
The derangement problem relative to the Mahonian process.
The discrete-time parabolic Anderson model with heavy-tailed potential
We consider a discrete-time version of the parabolic Anderson model. This may be described as a model for a directed -dimensional polymer interacting with a random potential, which is constant in the deterministic direction and i.i.d. in the orthogonal directions. The potential at each site is a positive random variable with a polynomial tail at infinity. We show that, as the size of the system diverges, the polymer extremity is localized almost surely at one single point which grows ballistically....