The structure of finite clusters in high intensity Poisson Boolean stick process
نویسندگان
چکیده
Sticks at one of different orientation are placed in an i.i.d. fashion at points of a Poisson point process of intensity λ. Sticks of the same direction have the same length, while sticks in different directions may have different lengths. We study the geometry of finite cluster as λ → ∞. The asymptotic shape of the custer being determined by the probabilities of the sticks in various direction and their lengths and orientations. We also obtain the limiting geometric structure of this component.
منابع مشابه
Propagation Models and Fitting Them for the Boolean Random Sets
In order to study the relationship between random Boolean sets and some explanatory variables, this paper introduces a Propagation model. This model can be applied when corresponding Poisson process of the Boolean model is related to explanatory variables and the random grains are not affected by these variables. An approximation for the likelihood is used to find pseudo-maximum likelihood esti...
متن کاملRefined convergence for the Boolean model
In a previous work [9] two of the authors proposed a new proof of a well known convergence result for the scaled elementary connected vacant component in the high intensity Boolean model towards the Crofton cell of the Poisson hyperplane process (see e.g. [4]). In this paper, we investigate the second-order term in this convergence when the two-dimensional Boolean model and the Poisson line pro...
متن کاملOn Laslett’s Transform for the Boolean Model
Consider the Boolean model in IR, where the germs form a homogeneous Poisson point process with intensity λ and the grains are convex compact random sets. It is known (see e.g. Section 9.5.3 in Cressie (1993)) that Laslett’s rule transforms the exposed tangent points of the Boolean model into a homogeneous Poisson process with the same intensity λ. In the present paper, we give a simple proof o...
متن کاملFractional Poisson Process
For almost two centuries, Poisson process with memoryless property of corresponding exponential distribution served as the simplest, and yet one of the most important stochastic models. On the other hand, there are many processes that exhibit long memory (e.g., network traffic and other complex systems). It would be useful if one could generalize the standard Poisson process to include these p...
متن کاملFinite Element Analysis of Tissue Conductivity during High-frequency and Low-voltage Irreversible Electroporation
Introduction: Irreversible electroporation (IRE) is a process in which the membrane of the cancer cells are irreversibly damaged with the use of high-intensity electric pulses, which in turn leads to cell death. The IRE is a non-thermal way to ablate the cancer cells. This process relies on the distribution of the electric field, which affects the pulse amplitude, width, and electrical conducti...
متن کامل