| Автор | C J G Evertsz |
| Автор | P W Jones |
| Автор | B B Mandelbrot |
| Дата выпуска | 1991-04-21 |
| dc.description | Diffusion-limited aggregates are among many important fractal shapes that involve deep indentations usually called fjords. To estimate the harmonic measure at the bottom of a fjord seems a prohibitive task, but the authors find that a new mathematical equality due to Beurling, Carleson and Jones makes it easy. They find that the harmonic measure at the bottom of a fjord, as a function of its Euclidean depth, can exhibit a wide range of behaviours. They introduce an infinite family of model fjords, for which the equality takes a very simple form. In this family the decay of the harmonic measure at their bottoms can be, for example, power law, semi-exponential, stretched exponential and exponentially stretched exponential. They show that self-affinity or randomness can lead to faster than power law decays of the minimal growth probability on boundaries. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | Behaviour of the harmonic measure at the bottom of fjords |
| Тип | paper |
| DOI | 10.1088/0305-4470/24/8/028 |
| Print ISSN | 0305-4470 |
| Журнал | Journal of Physics A: Mathematical and General |
| Том | 24 |
| Первая страница | 1889 |
| Последняя страница | 1901 |
| Аффилиация | C J G Evertsz; Dept. of Appl. Phys., Yale Univ., New Haven, CT, USA |
| Аффилиация | P W Jones; Dept. of Appl. Phys., Yale Univ., New Haven, CT, USA |
| Аффилиация | B B Mandelbrot; Dept. of Appl. Phys., Yale Univ., New Haven, CT, USA |
| Выпуск | 8 |
