{"paper":{"title":"The inertial It\\^o drift and its applications to particle collision","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The small-mass limit of inertial particles driven by Ornstein-Uhlenbeck forces produces an extra inertial Itô drift whose strength depends on the ratio of mass to correlation time.","cross_cats":[],"primary_cat":"math.PR","authors_text":"Franco Flandoli, Mengzi Xie, Sandra Cerrai","submitted_at":"2026-05-13T13:35:17Z","abstract_excerpt":"The small mass $\\mu$ limit of an inertial system driven by an Ornstein Uhlenbeck fluid force, with correlation time $\\epsilon$ going to zero, leads to a first order system with an additional drift, which we call inertial-It\\^{o}-drift, depending on the limit $\\alpha$ of the ratio $\\mu/\\epsilon$; the drift being zero when $\\alpha=0$, corresponding to the Stratonovich integral in the limit equation, as in the Wong-Zakai theory, when applied directly to the first-order system with Ornstein-Uhlenbeck driver. We discuss the application of this result to particles driven by Stokes force;\\ we identif"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The small mass μ limit of an inertial system driven by an Ornstein Uhlenbeck fluid force, with correlation time ε going to zero, leads to a first order system with an additional drift, which we call inertial-Itô-drift, depending on the limit α of the ratio μ/ε; the drift being zero when α=0, corresponding to the Stratonovich integral in the limit equation, as in the Wong-Zakai theory.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the driving force is an Ornstein-Uhlenbeck process and that the double limit is taken with μ/ε → α, allowing the application of Wong-Zakai type results to the inertial system.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The inertial Itô drift emerges in the limiting first-order equation for small-mass particles in Ornstein-Uhlenbeck driven flows, vanishing only for zero mass-to-correlation-time ratio and corresponding to Stratonovich calculus.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The small-mass limit of inertial particles driven by Ornstein-Uhlenbeck forces produces an extra inertial Itô drift whose strength depends on the ratio of mass to correlation time.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ba3897e93c859ae28f5bd4c513fc1c1e0d9d05d02e1403b34714b076fa0a3ec2"},"source":{"id":"2605.13518","kind":"arxiv","version":1},"verdict":{"id":"0c728552-defb-4189-aeda-6ea145d844ea","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:18:31.064099Z","strongest_claim":"The small mass μ limit of an inertial system driven by an Ornstein Uhlenbeck fluid force, with correlation time ε going to zero, leads to a first order system with an additional drift, which we call inertial-Itô-drift, depending on the limit α of the ratio μ/ε; the drift being zero when α=0, corresponding to the Stratonovich integral in the limit equation, as in the Wong-Zakai theory.","one_line_summary":"The inertial Itô drift emerges in the limiting first-order equation for small-mass particles in Ornstein-Uhlenbeck driven flows, vanishing only for zero mass-to-correlation-time ratio and corresponding to Stratonovich calculus.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the driving force is an Ornstein-Uhlenbeck process and that the double limit is taken with μ/ε → α, allowing the application of Wong-Zakai type results to the inertial system.","pith_extraction_headline":"The small-mass limit of inertial particles driven by Ornstein-Uhlenbeck forces produces an extra inertial Itô drift whose strength depends on the ratio of mass to correlation time."},"references":{"count":17,"sample":[{"doi":"","year":2024,"title":"J. Bec, K. Gustavsson, B. Mehlig,Statistical models for the dynamics of heavy particles in turbulence, Annu. Rev. Fluid Mech. 56 (2024), pp. 189–213","work_id":"fcf6b589-d08f-46f5-a825-7fd2ecce3647","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2006,"title":"C. L. Berselli, T. Iliescu, J. W. Layton,Mathematics of Large Eddy Simulation of Turbulent Flows, Springer, 2006","work_id":"877703d3-b5db-4782-8f09-b9740ec886ea","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Boussinesq,Essai sur la th´ eorie des eaux courantes, M´ emoires pr´ esent´ es par divers savants a l’Academie des Sciences de l’Institut National de France, XXIII (1), (1877)","work_id":"34df87fc-50e6-4e96-b110-a491a7f36e76","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"Cerrai,A Khasminskii type averaging principle for stochastic reaction-diffusion equations, Annals of Applied Probability 19 (2009), pp","work_id":"303edd4a-64d6-4755-b885-31302e6fa8b3","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"F. De Lillo, M. Cencini, S. Musacchio, G. Boffetta,Clustering and turbophoresis in a shear flow without walls, Physics of Fluids 28 (2016)","work_id":"797dda36-363d-41c0-b85b-887a1ad8fc27","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":17,"snapshot_sha256":"78c8a59588179afd6ad3b6059feef32424e8bb686db7444f0c443a1e53be6b11","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"}