%0 Generic %1 penrose2010local %A Penrose, Mathew D. %A Peres, Yuval %D 2010 %K dependant_CLT local_CLT percolation %T Local central limit theorems in stochastic geometry %U http://arxiv.org/abs/1006.3523 %X We give a general local central limit theorem for the sum of two independent random variables, one of which satisfies a central limit theorem while the other satisfies a local central limit theorem with the same order variance. We apply this result to various quantities arising in stochastic geometry, including: size of the largest component for percolation on a box; number of components, number of edges, or number of isolated points, for random geometric graphs; covered volume for germ-grain coverage models; number of accepted points for finite-input random sequential adsorption; sum of nearest-neighbour distances for a random sample from a continuous multidimensional distribution.

@misc{penrose2010local, abstract = { We give a general local central limit theorem for the sum of two independent random variables, one of which satisfies a central limit theorem while the other satisfies a local central limit theorem with the same order variance. We apply this result to various quantities arising in stochastic geometry, including: size of the largest component for percolation on a box; number of components, number of edges, or number of isolated points, for random geometric graphs; covered volume for germ-grain coverage models; number of accepted points for finite-input random sequential adsorption; sum of nearest-neighbour distances for a random sample from a continuous multidimensional distribution. }, added-at = {2010-06-23T18:39:35.000+0200}, author = {Penrose, Mathew D. and Peres, Yuval}, biburl = {https://www.bibsonomy.org/bibtex/2e69f6e93bb9af2fe58fb8ebd437954fd/peter.ralph}, description = {[1006.3523] Local central limit theorems in stochastic geometry}, interhash = {12e6e2ea4ebe64f08d284f18221c20b1}, intrahash = {e69f6e93bb9af2fe58fb8ebd437954fd}, keywords = {dependant_CLT local_CLT percolation}, note = {cite arxiv:1006.3523 Comment: 31 Pages}, timestamp = {2010-06-23T18:39:35.000+0200}, title = {Local central limit theorems in stochastic geometry}, url = {http://arxiv.org/abs/1006.3523}, year = 2010 }