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Optimal estimates of the diffusion coefficient of a single Brownian trajectory

hal.structure.identifierInstituto de Fisica
dc.contributor.authorBOYER, Denis
hal.structure.identifierLaboratoire Ondes et Matière d'Aquitaine [LOMA]
dc.contributor.authorDEAN, David S.
hal.structure.identifierLaboratory of Physical Properties
dc.contributor.authorMEJÍA-MONASTERIO, Carlos
hal.structure.identifierLaboratoire de Physique Théorique de la Matière Condensée [LPTMC]
dc.contributor.authorOSHANIN, Gleb
dc.date.created2012-01-11
dc.date.issued2012
dc.identifier.issn1539-3755
dc.description.abstractEnModern developments in microscopy and image processing are revolutionizing areas of physics, chemistry and biology as nanoscale objects can be tracked with unprecedented accuracy. The goal of single particle tracking is to determine the interaction between the particle and its environment. The price paid for having a direct visualization of a single particle is a consequent lack of statistics. Here we address the optimal way of extracting diffusion constants from single trajectories for pure Brownian motion. It is shown that the maximum likelihood estimator is much more efficient than the commonly used least squares estimate. Furthermore we investigate the effect of disorder on the distribution of estimated diffusion constants and show that it increases the probability of observing estimates much smaller than the true (average) value.
dc.language.isoen
dc.publisherAmerican Physical Society
dc.subject.enBrownian motion
dc.subject.enPath-integral methods
dc.title.enOptimal estimates of the diffusion coefficient of a single Brownian trajectory
dc.typeArticle de revue
dc.identifier.doi10.1103/PhysRevE.85.031136
dc.subject.halPhysique [physics]/Matière Condensée [cond-mat]/Mécanique statistique [cond-mat.stat-mech]
dc.identifier.arxiv1203.5038
bordeaux.journalPhysical Review E : Statistical, Nonlinear, and Soft Matter Physics
bordeaux.page031136
bordeaux.volume85
bordeaux.issue3
bordeaux.peerReviewedoui
hal.identifierhal-00696477
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00696477v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Physical%20Review%20E%20:%20Statistical,%20Nonlinear,%20and%20Soft%20Matter%20Physics&rft.date=2012&rft.volume=85&rft.issue=3&rft.spage=031136&rft.epage=031136&rft.eissn=1539-3755&rft.issn=1539-3755&rft.au=BOYER,%20Denis&DEAN,%20David%20S.&MEJ%C3%8DA-MONASTERIO,%20Carlos&OSHANIN,%20Gleb&rft.genre=article


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