On Geary’s theorem for the field of p-adic numbers
| Autor: | Margaryta Myronyuk, Gennadiy Feldman |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Independent and identically distributed random variables
Indecomposable distribution General Mathematics 010102 general mathematics 01 natural sciences Combinatorics Infinite divisibility (probability) 0103 physical sciences Sum of normally distributed random variables Illustration of the central limit theorem Irwin–Hall distribution 010307 mathematical physics 0101 mathematics Mathematics Central limit theorem p-adic number |
| Zdroj: | Doklady Mathematics. 93:152-154 |
| ISSN: | 1531-8362 1064-5624 |
| DOI: | 10.1134/s1064562416020095 |
| Popis: | Let ℚp, where p > 2, be a field of p-adic numbers. We consider two independent identically distributed random variables with values in ℚp and distribution μ with a continuous density. We prove that the sum and the squared difference of these random variables are independent if and only if μ is an idempotent distribution, i.e., a shift of the Haar distribution of a compact subgroup of the additive group of the field ℚp. |
| Databáze: | OpenAIRE |
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