Random Walks of Circle Packings
نویسندگان
چکیده
A notion of random walks for circle packings is introduced. The geometry behind this notion is discussed, together with some applications. In particular, we obtain a short proof of a result regarding the type problem for circle packings, which shows that the type of a circle packing is closely related to the type of its tangency graph.
منابع مشابه
1 6 A ug 1 99 5 RANDOM WALKS OF CIRCLE PACKINGS
A notion of random walks for circle packings is introduced. The geometry behind this notion is discussed, together with some applications. In particular, we obtain a short proof of a result regarding the type problem for circle packings, which shows that the type of a circle packing is closely related to the type of its tangency graph.
متن کاملRandom Walks , Liouville ' S Theorem , and Circle Packings
It has been shown that univalent circle packings lling in the complex plane C are unique up to similarities of C. Here we prove that bounded degree branched circle packings properly covering C are uniquely determined, up to similarities of C, by their branch sets. In particular, when branch sets of the packings considered are empty we obtain the earlier result. We also establish a circle packin...
متن کامل1 0 M ay 1 99 5 RECURRENT RANDOM WALKS , LIOUVILLE ’ S THEOREM , AND CIRCLE PACKINGS
It has been shown that univalent circle packings filling in the complex plane C are unique up to similarities of C. Here we prove that bounded degree branched circle packings properly covering C are uniquely determined, up to similarities of C, by their branch sets. In particular, when branch sets of the packings considered are empty we obtain the earlier result. We also establish a circle pack...
متن کاملRandom Walks on Discrete and Continuous Circles
We consider a large class of random walks on the discrete circle Z/(n), defined in terms of a piecewise Lipschitz function, and motivated by the “generation gap” process of Diaconis. For such walks, we show that the time until convergence to stationarity is bounded independently of n. Our techniques involve Fourier analysis and a comparison of the random walks on Z/(n) with a random walk on the...
متن کاملRandom Walks on Discrete and Continuous
We consider a large class of random walks on the discrete circle Z=(n), deened in terms of a piecewise Lipschitz function, and motivated by the \generation gap" process of Diaconis. For such walks, we show that the time until convergence to stationarity is bounded independently of n. Our techniques involve Fourier analysis and a comparison of the random walks on Z=(n) with a random walk on the ...
متن کامل