{"id":"openai-math/Independent-products-in-real-L1-asymptotic-midpoint-convexity-without-AUC-renormings","pdf":"https://github.com/openai/math/blob/main/preprints/Independent-products-in-real-L1-asymptotic-midpoint-convexity-without-AUC-renormings-September-27-2026/manuscript.pdf","url":"https://github.com/openai/math/tree/main/preprints/Independent-products-in-real-L1-asymptotic-midpoint-convexity-without-AUC-renormings-September-27-2026","tags":["functional-analysis","banach-spaces","probability"],"score":0,"title":"Independent products in real L1: asymptotic midpoint convexity without AUC renormings","domain":"Functional analysis","family":"331","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.FA","summary":"For a countably branching tree, the closed real L 1 spans of products of independent exponential or Gaussian-square multipliers along its paths have positive averaged asymptotic midpoint moduli and admit no equivalent asymptotically uniformly convex norm. The renorming obstruction holds for every positive nonconstant mean-one multiplier with finite second moment.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-27","reactions":{},"formalized":true,"family_title":"Reflexive midpoint convexity and diamond distortion"}