Discrete Morse theory for random complexes (Record no. 373541)

000 -LEADER
fixed length control field 02446ntm a22003257a 4500
003 - CONTROL NUMBER IDENTIFIER
control field AT-ISTA
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20190813103052.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 180627s2017 au ||||| m||| 00| 0 eng d
040 ## - CATALOGING SOURCE
Transcribing agency IST
100 ## - MAIN ENTRY--PERSONAL NAME
Personal name Nikitenko, Anton
9 (RLIN) 4269
245 ## - TITLE STATEMENT
Title Discrete Morse theory for random complexes
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Name of publisher, distributor, etc. IST Austria
Date of publication, distribution, etc. 2017
500 ## - GENERAL NOTE
General note Thesis
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Formatted contents note Abstract
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Formatted contents note Acknowledgments
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Formatted contents note List of publications
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Formatted contents note 1 Introduction
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Formatted contents note 2 Results
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Formatted contents note 3 Blaschke- Petkantschin formulas
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Formatted contents note 4 Constants
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Formatted contents note 5 Poisson-Delaunay, Poisson-Čech and weighted Poisson-Delaunay complexes
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Formatted contents note 6 Poisson-Delaunay complexes of higher order
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Formatted contents note 7 Random inscribed polytops
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Formatted contents note 8 Future directions
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Formatted contents note Bibliography
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Formatted contents note Index
520 ## - SUMMARY, ETC.
Summary, etc. The main objects considered in the present work are simplicial and CW-complexes with vertices forming a random point cloud.<br/> In particular, we consider a Poisson point process in R^n<br/> and study Delaunay and Voronoi complexes of the first and higher orders and weighted Delaunay complexes obtained as sections of Delaunay complexes, as well as the Čech complex.<br/> Further, we examine theDelaunay complex of a Poisson<br/> point process on the sphere S^n, as well as of a uniform point cloud, which is equivalent to the convex hull, providing a connection to the theory of random polytopes.<br/> <br/> Each of the complexes in question can be endowed with a radius function,<br/> which maps its cells to the radii of appropriately chosen circumspheres,<br/> called the radius of the cell.<br/> Applying and developing discrete Morse theory for these functions, joining it together with probabilistic and sometimes analytic machinery, and developing several integral geometric tools, we aim at getting the distributions of circumradii of typical cells.<br/> For all considered complexes, we are able to generalize and obtain up to constants <br/> the distribution of radii of typical intervals of all types.<br/> In low dimensions the constants<br/> can be computed explicitly, thus providing the explicit<br/> expressions for the expected numbers of cells.<br/> In particular, it allows to find the expected density of simplices<br/> of every dimension for a Poisson point process in R^4,<br/> whereas the result for R^3 was known already in 1970's.
856 ## - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://doi.org/10.15479/AT:ISTA:th_873">https://doi.org/10.15479/AT:ISTA:th_873</a>
942 ## - ADDED ENTRY ELEMENTS (KOHA)
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  Not Lost       Library Library 2018-06-27 AT-ISTA#001531 2018-11-06 2018-06-27 Book

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