{"id":"palomar/PALOMAR-2026-09-20-000007","url":"https://github.com/Vulkin-prog/paper-c-lean/tree/d8edbc44654f623fc68df92612c26a6ef9a90ec2","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-20-000007-v1.json","repo":"https://github.com/Vulkin-prog/paper-c-lean","tags":["math.NT","math.PR","msc:11K65","msc:60F05","probability","number-theory","gaussian-limits"],"score":0,"title":"Threshold staircases and the Poisson–Gaussian bridge","trust":"high","domain":"math.NT","source":"palomar","authors":["Brice Pouly"],"reviews":0,"subject":"math.NT","summary":"Joint Poisson–Gaussian limits for conditioned run counts, with an autoregressive Gaussian target and independent normal innovations. Quantitative results give local Poisson probabilities, a Gaussian distribution-function bound, moderate deviations, and relative local or tail estimates for the multiplicative source under the stated information budgets. The whole integer-level point process has locally finite but infinite total mass; its complete upper-half laws, conditioning on a fixed count and extreme phases are included. The two upper-half law assertions include proved measurability and…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-20","reactions":{},"formalized":true,"formalizes":[{"title":"Long runs and rare patterns of a random completely multiplicative function","identifier":"https://github.com/Vulkin-prog/paper-c-lean/blob/b3cf9aa27700d784efc61e6f82a92cef53320c40/manuscripts/paper-c/paper_c_version_3PREL9_en.pdf","relationship":"adapts"},{"title":"Technical companion to Long runs and rare patterns of a random completely multiplicative function","identifier":"https://github.com/Vulkin-prog/paper-c-lean/blob/b3cf9aa27700d784efc61e6f82a92cef53320c40/manuscripts/paper-c/paper_c_version_3PREL9_technical_companion_en.pdf","relationship":"adapts"}]}