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Given a $G$--valued random matrix $A$, we consider the following generalized multidimensional affine equation\nR\\stackrel{\\mathcal{D}}{=}\\sum_{i=1}^N A_iR_i+B,\nwhere $N\\ge2$ is a fixed natural number, $A_1,...,A_N$ are independent copies of $A$, $B\\in\\mathbb{R}^d$ is a random vector with positive entries, and $R_1,...,R_N$ are independent copies of $R\\in\\mathbb{R}^d$, which have also p"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1111.1756","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-07T21:50:31Z","cross_cats_sorted":[],"title_canon_sha256":"2c105bada813de36560461acd5af173a4c2ec068564501597f1b7d245c527664","abstract_canon_sha256":"273f03b1c27e80cd3c3cdb421f793bf7a74fd4711a24304483008d5e763545ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:24.786034Z","signature_b64":"vZA5yon19zI8fBpDZ3Jkiqf6v3hP9qXNmQYc2PiPC7y34hPHhrkLSQuNOO2CvVeXlaqZUUcIZsW1qeZAY7zEDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9922555441a28a4ab1aa7b241de3129dae7617b29b9a7678c79ed7e635e006a","last_reissued_at":"2026-05-18T04:09:24.785314Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:24.785314Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On fixed points of a generalized multidimensional affine recursion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mariusz Mirek","submitted_at":"2011-11-07T21:50:31Z","abstract_excerpt":"Let $G$ be a multiplicative subsemigroup of the general linear group $\\Gl(\\mathbb{R}^d)$ which consists of matrices with positive entries such that every column and every row contains a strictly positive element. 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