2016
DOI: 10.1007/s00332-016-9327-4
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The Algebro-geometric Study of Range Maps

Abstract: In this paper, we study the combined mean field and homogenization limits for a system of weakly interacting diffusions moving in a two-scale, locally periodic confining potential, of the form considered in Duncan et al. (Brownian motion in an N-scale periodic potential, arXiv:1605.05854, 2016b). We show that, although the mean field and homogenization limits commute for finite times, they do not, in general, commute in the long time limit. In particular, the bifurcation diagrams for the stationary states can … Show more

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Cited by 9 publications
(13 citation statements)
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References 55 publications
(127 reference statements)
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“…This map was thoroughly studied in [19], [21], in the context of planar source localization. Furthermore, in [22] (Remark 10.4) is the proof that…”
Section: The Case N =mentioning
confidence: 99%
See 1 more Smart Citation
“…This map was thoroughly studied in [19], [21], in the context of planar source localization. Furthermore, in [22] (Remark 10.4) is the proof that…”
Section: The Case N =mentioning
confidence: 99%
“…If G = Σ −1 , (21) and (22) are known in the statistical literature as the Mahalanobis product and norm, respectively.…”
Section: A Statistical Noise Modelmentioning
confidence: 99%
“…Remark 4.8. The locus of L 2,4 where the edge lengths of a triangle, (l 12 , l 13 , l 23 ), are held fixed is studied in beautiful detail in [8], where this is shown to be a Kummer surface.…”
Section: Measurement Varietiesmentioning
confidence: 99%
“…Ho and Chan [11] provided a first development of equations for using TDOA measurements to back out emitter location, coming very close to the polynomial system development given in the next section. The more recent articles [7], [8] provide an advanced description of this TDOA-only setting, based largely on algebraic geometry. Various other approaches have been developed, and at least one [14] has made use of numerical algebraic geometry, though in a rather different context.…”
Section: Introductionmentioning
confidence: 99%