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On the Distribution function of area and perimeter for planar poisson line processтезисы доклада
- Авторы: Kanel-Belov Alexey, Golafshan Mehdi, Malev Sergey, Yavich Roman
- Сборник: Functional Differential Equations and Applications
- Тезисы
- Год издания: 2022
- Место издания: Ariel University Ariel
- Первая страница: 15
- Последняя страница: 16
- Аннотация: The challenges of examining random partitions of space are a significant class of problems in the theory of geometric transformations. RichardMiles calculated moments of areas and perimeters of any order (includingexpectation) of the random division of space in 1972. In the paper wecalculate the whole distribution function of random divisions of the planeby poisson line process.The idea is to interpret a random polygon as the evolution of a segmentalong a moving straight line. In the plane example, the issue connectedwith an infinite number of parameters is overcome by considering a secantline. We shall take into account the following tasks:1. On the plane, a random set of straight lines is provided, all shiftsare equally likely, and the distribution law is of the form F(φ). What isthe area distribution of the partition’s components?2. On the plane, a random set of points is marked. Each point A hasan associated area of attraction, which is the collection of points in theplane to which the point A is the nearest of the designated ones. In thefirst problem, the density of moved sections adjacent to the line allows forthe expression of the balancing ratio in kinetic form. Similarly, you canwrite the perimeters kinetic equations. We will demonstrate how to reducethese equations to the Riccati equation using the Laplace transformation.
- Добавил в систему: Белов Алексей Яковлевич
Прикрепленные файлы
| № | Имя | Описание | Имя файла | Размер | Добавлен |
|---|---|---|---|---|---|
| 1. | Краткий текст | номер где статья | FDEA_2022_Program_and_Abstracts_september_12_2022.pdf | 354,6 КБ | 16 сентября 2022 [AlexeiBelov] |
| 2. | Презентация | conf-talk.pdf | 397,5 КБ | 20 сентября 2022 [AlexeiBelov] |