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020 _a9783031541049
_9978-3-031-54104-9
024 7 _a10.1007/978-3-031-54104-9
_2doi
050 4 _aQA440-699
072 7 _aPBM
_2bicssc
072 7 _aMAT012000
_2bisacsh
072 7 _aPBM
_2thema
100 1 _aHug, Daniel.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_977285
245 1 0 _aPoisson Hyperplane Tessellations
_h[electronic resource] /
_cby Daniel Hug, Rolf Schneider.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXI, 550 p. 27 illus., 26 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Monographs in Mathematics,
_x2196-9922
505 0 _a- 1 Notation -- 2 Hyperplane and particle processes -- 3 Distribution-independent density relations -- 4 Poisson hyperplane processes -- 5 Auxiliary functionals and bodies -- 6 Zero cell and typical cell -- 7 Mixing and ergodicity -- 8 Observations inside a window -- 9 Central limit theorems -- 10 Palm distributions and related constructions -- 11 Typical faces and weighted faces -- 12 Large cells and faces -- 13 Cells with a given number of facets -- 14 Small cells -- 15 The K-cell under increasing intensities -- 16 Isotropic zero cells -- 17 Functionals of Poisson processes and applications -- 18 Appendix: Some auxiliary results.
520 _aThis book is the first comprehensive presentation of a central topic of stochastic geometry: random mosaics that are generated by Poisson processes of hyperplanes. It thus connects a basic notion from probability theory, Poisson processes, with a fundamental object of geometry. The independence properties of Poisson processes and the long-range influence of hyperplanes lead to a wide range of phenomena which are of interest from both a geometric and a probabilistic point of view. A Poisson hyperplane tessellation generates many random polytopes, also a much-studied object of stochastic geometry. The book offers a variety of different perspectives and covers in detail all aspects studied in the original literature. The work will be useful to graduate students (advanced students in a Master program, PhD students), and professional mathematicians. The book can also serve as a reference for researchers in fields of physics, computer science, economics or engineering.
650 0 _aGeometry.
_968763
650 0 _aStochastic processes.
_976770
650 1 4 _aGeometry.
_968763
650 2 4 _aStochastic Processes.
_976770
700 1 _aSchneider, Rolf.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_977286
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031541032
776 0 8 _iPrinted edition:
_z9783031541056
776 0 8 _iPrinted edition:
_z9783031541063
830 0 _aSpringer Monographs in Mathematics,
_x2196-9922
_973001
856 4 0 _uhttps://doi.org/10.1007/978-3-031-54104-9
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c60061
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