{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:EW3HK7MMEDNH23OD5KWBBBYSF7","short_pith_number":"pith:EW3HK7MM","schema_version":"1.0","canonical_sha256":"25b6757d8c20da7d6dc3eaac1087122fdcd1f276d77ad63f913eb949d589d0a6","source":{"kind":"arxiv","id":"1305.1442","version":1},"attestation_state":"computed","paper":{"title":"On the Distribution of Random variables corresponding to Musielak-Orlicz norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"David Alonso-Gutierrez, Joscha Prochno, Markus Passenbrunner, Soeren Christensen","submitted_at":"2013-05-07T08:57:12Z","abstract_excerpt":"Given a normalized Orlicz function $M$ we provide an easy formula for a distribution such that, if $X$ is a random variable distributed accordingly and $X_1,...,X_n$ are independent copies of $X$, then the expected value of the p-norm of the vector $(x_iX_i)_{i=1}^n$ is of the order $\\| x \\|_M$ (up to constants dependent on p only). In case $p=2$ we need the function $t\\mapsto tM'(t) - M(t)$ to be 2-concave and as an application immediately obtain an embedding of the corresponding Orlicz spaces into $L_1[0,1]$. We also provide a general result replacing the $\\ell_p$-norm by an arbitrary $N$-no"},"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":"1305.1442","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-05-07T08:57:12Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"d56b3b11f71d68d15139ac9b5da92c0e632d7096c66365f1a5c7d5cf4489c073","abstract_canon_sha256":"132185f408130268c08af5dadd3342c3bf17131556fd6c78af7f65b0a952ce6a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:49.339020Z","signature_b64":"cqFSmK7cd6xboqGOfqLtLAtgCpyTFF3lnEP4qbXwj/hmPXMgjNwvC2IHZcYQTbC8pFOkTQIqvKefCvp3YKfxBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25b6757d8c20da7d6dc3eaac1087122fdcd1f276d77ad63f913eb949d589d0a6","last_reissued_at":"2026-05-18T02:25:49.338643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:49.338643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Distribution of Random variables corresponding to Musielak-Orlicz norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"David Alonso-Gutierrez, Joscha Prochno, Markus Passenbrunner, Soeren Christensen","submitted_at":"2013-05-07T08:57:12Z","abstract_excerpt":"Given a normalized Orlicz function $M$ we provide an easy formula for a distribution such that, if $X$ is a random variable distributed accordingly and $X_1,...,X_n$ are independent copies of $X$, then the expected value of the p-norm of the vector $(x_iX_i)_{i=1}^n$ is of the order $\\| x \\|_M$ (up to constants dependent on p only). In case $p=2$ we need the function $t\\mapsto tM'(t) - M(t)$ to be 2-concave and as an application immediately obtain an embedding of the corresponding Orlicz spaces into $L_1[0,1]$. We also provide a general result replacing the $\\ell_p$-norm by an arbitrary $N$-no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1442","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1305.1442","created_at":"2026-05-18T02:25:49.338700+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.1442v1","created_at":"2026-05-18T02:25:49.338700+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1442","created_at":"2026-05-18T02:25:49.338700+00:00"},{"alias_kind":"pith_short_12","alias_value":"EW3HK7MMEDNH","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"EW3HK7MMEDNH23OD","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"EW3HK7MM","created_at":"2026-05-18T12:27:43.054852+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EW3HK7MMEDNH23OD5KWBBBYSF7","json":"https://pith.science/pith/EW3HK7MMEDNH23OD5KWBBBYSF7.json","graph_json":"https://pith.science/api/pith-number/EW3HK7MMEDNH23OD5KWBBBYSF7/graph.json","events_json":"https://pith.science/api/pith-number/EW3HK7MMEDNH23OD5KWBBBYSF7/events.json","paper":"https://pith.science/paper/EW3HK7MM"},"agent_actions":{"view_html":"https://pith.science/pith/EW3HK7MMEDNH23OD5KWBBBYSF7","download_json":"https://pith.science/pith/EW3HK7MMEDNH23OD5KWBBBYSF7.json","view_paper":"https://pith.science/paper/EW3HK7MM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.1442&json=true","fetch_graph":"https://pith.science/api/pith-number/EW3HK7MMEDNH23OD5KWBBBYSF7/graph.json","fetch_events":"https://pith.science/api/pith-number/EW3HK7MMEDNH23OD5KWBBBYSF7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EW3HK7MMEDNH23OD5KWBBBYSF7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EW3HK7MMEDNH23OD5KWBBBYSF7/action/storage_attestation","attest_author":"https://pith.science/pith/EW3HK7MMEDNH23OD5KWBBBYSF7/action/author_attestation","sign_citation":"https://pith.science/pith/EW3HK7MMEDNH23OD5KWBBBYSF7/action/citation_signature","submit_replication":"https://pith.science/pith/EW3HK7MMEDNH23OD5KWBBBYSF7/action/replication_record"}},"created_at":"2026-05-18T02:25:49.338700+00:00","updated_at":"2026-05-18T02:25:49.338700+00:00"}