Everything about Geometric discrepancy
Geometric discrepancy theory is a sub-field of discrepancy theory, that deals with balancing points in geometric sets, such as intervals or rectangles. Two closely-related research questions in this field are:Two-color discrepancy: Given a set of objects in a geometric space, and a set of points in the same space, can we color each point in one of two different colors, such that each object contains roughly the same number of points of each color? Formally, the discrepancy of an object is defined as the difference between the number of white points and the number of black points in that object; the goal is to color the points such that the maximum discrepancy of an object is as small as possible. Expected-value discrepancy : Given a set of objects in a geometric space, and an integer N, can we design a set of N points, such that each object contains a fraction of the points that is roughly proportional to its size? Formally, the discrepancy of an object is defined as the difference between the number of points in that object, and the expected number of points if the points were distributed uniformly at random; the goal is to find a set of points such that the maximum discrepancy of an object is as small as possible. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Geometric discrepancyA 5-minute orientation
- Skim a recent paper: Flat-band Fulde-Ferrell-Larkin-Ovchinnikov state from quantum geometric discrepancyInfluential work since 2022
- Pick up a classic book: Sampling in Combinatorial and Geometric Set SystemsThe most-reprinted book on the subject
- Read the landmark paper: Bracketing numbers for axis-parallel boxes and applications to geometric discrepancyCited 42 times
- Go sideways: Discrepancy theoryA closely related topic
- Go sideways: Moment curveA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Bracketing numbers for axis-parallel boxes and applications to geometric discrepancy
Learning geometric consistency and discrepancy for category-level 6D object pose estimation from point clouds
Using low-discrepancy sequences and the Crofton formula to compute surface areas of geometric models
Economic Uncertainty: A Geometric Indicator of Discrepancy Among Experts’ Expectations
Quasirandom geometric networks from low-discrepancy sequences
Metric discrepancy results for alternating geometric progressions
Metric discrepancy results for geometric progressions with large ratios
Geometric Characterization of Weyl’s Discrepancy Norm in Terms of Its n-Dimensional Unit Balls
🆕 Influential since 2022
Flat-band Fulde-Ferrell-Larkin-Ovchinnikov state from quantum geometric discrepancy
A method for measuring geometric information content of area cartographic objects based on discrepancy degree of shape points
Metric discrepancy results for geometric progressions with large ratios II
Polynomial‐order oscillations in geometric discrepancy
Metric star discrepancy results for alternating geometric progressions
📚 Books worth reading
- 📕Sampling in Combinatorial and Geometric Set SystemsNabil H. Mustafa · 2022
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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