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An Application of the Renormalization Group Method to Stable Limit Laws |
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| Authors: | Dong Li Yakov G. Sinai |
| Affiliation: | 1. Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, V6T1Z2, Canada 2. Mathematics Department, Princeton University, Princeton, NJ, 08544, USA 3. Landau Institute of Theoretical Physics, Moscow, Russia |
| Abstract: | Let ((X_n)_{n=1}^{infty }) be a sequence of independent identically distributed random variables. We study the normalized partial sums and the corresponding renormalization group flow in the space of probability densities. We prove the convergence to stable limit laws under suitable assumptions on the initial density. |
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