{"ID":2834519,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.01689","arxiv_id":"2512.01689","title":"The Klebanov theorem for the group $\\mathbb{R}\\times \\mathbb{Z}(2)$","abstract":"L. Klebanov proved the following theorem. Let $ξ_1, \\dots, ξ_n$ be independent random variables. Consider linear forms $L_1=a_1ξ_1+\\cdots+a_nξ_n,$ $L_2=b_1ξ_1+\\cdots+b_nξ_n,$ $L_3=c_1ξ_1+\\cdots+c_nξ_n,$ $L_4=d_1ξ_1+\\cdots+d_nξ_n,$ where the coefficients $a_j, b_j, c_j, d_j$ are real numbers. If the random vectors $(L_1,L_2)$ and $(L_3,L_4)$ are identically distributed, then all $ξ_i$ for which $a_id_j-b_ic_j\\neq 0$ for all $j=\\overline{1,n}$ are Gaussian random variables. The present article is devoted to an analogue of the Klebanov theorem in the case when random variables take values in the group $\\mathbb{R}\\times \\mathbb{Z}(2)$ and the coefficients of the linear forms are topological endomorphisms of this group.","short_abstract":"L. Klebanov proved the following theorem. Let $ξ_1, \\dots, ξ_n$ be independent random variables. Consider linear forms $L_1=a_1ξ_1+\\cdots+a_nξ_n,$ $L_2=b_1ξ_1+\\cdots+b_nξ_n,$ $L_3=c_1ξ_1+\\cdots+c_nξ_n,$ $L_4=d_1ξ_1+\\cdots+d_nξ_n,$ where the coefficients $a_j, b_j, c_j, d_j$ are real numbers. If the random vectors $(L_1...","url_abs":"https://arxiv.org/abs/2512.01689","url_pdf":"https://arxiv.org/pdf/2512.01689v1","authors":"[\"Margaryta Myronyuk\"]","published":"2025-12-01T13:57:30Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.ST\"]","methods":"[]","has_code":false}