Limit distributions and scaling functions

Richard C (2009)

Publication Type: Book chapter / Article in edited volumes

Publication year: 2009

Publisher: Springer

Edited Volumes: Polygons, polyominoes and polycubes

Series: Lecture Notes in Physics

City/Town: Dordrecht

Book Volume: 775

Pages Range: 247-299

ISBN: 978-1-4020-9926-7

DOI: 10.1007/978-1-4020-9927-4_11

Abstract

For a given combinatorial class of objects, such as polygons or polyhedra, the most basic question concerns the number of objects of a given size (always assumed to be finite), or an asymptotic estimate thereof. Informally stated, in this overview we will analyse the refined question:

What does a typical object look like?

In contrast to the combinatorial question about the number of objects of a given size, the latter question is of a probabilistic nature. For counting parameters in addition to object size, one asks for their (asymptotic) probability law. To give this question a meaning, an underlying ensemble has to be specified. The simplest choice is the uniform ensemble, where each object of a given size occurs with equal probability.

 

Authors with CRIS profile

Christoph Richard Lehrstuhl für Mathematische Stochastik

How to cite

APA:

Richard, C. (2009). Limit distributions and scaling functions. In Anthony J. Guttmann (Eds.), Polygons, polyominoes and polycubes. (pp. 247-299). Dordrecht: Springer.

MLA:

Richard, Christoph. "Limit distributions and scaling functions." Polygons, polyominoes and polycubes. Ed. Anthony J. Guttmann, Dordrecht: Springer, 2009. 247-299.

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