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Statistics of two-dimensional random wal...

Mashkevich, Stefan...

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Statistics of two-dimensional random walks, the "cyclic sieving phenomenon" and the Hofstadter model by Mashkevich, Stefan ( Author )

Content Provider	Lemonjar Open Access
Publisher	N.A
Publication Date	22-04-2015
Summary	We focus on the algebraic area probability distribution of planar random walks on a square lattice with m1, m2, l1 and l2 steps right, left, up and down. We aim, in particular, at the algebraic area generating function Zm1,m2,l1,l2(Q) evaluated at Q=e2ıπq, a root of unity, when both m1−m2 and l1−l2 are multiples of q. In the simple case of staircase walks, a geometrical interpretation of Zm,0,l,0(e2iπq) in terms of the cyclic sieving phenomenon is illustrated. Then, an expression for Zm1,m2,l1,l2(−1), which is relevant to the Stembridge's case, is proposed. Finally, the related problem of evaluating the n-th moments of the Hofstadter Hamiltonian in the commensurate case is addressed.
ISBN	-
Item Type	Article
File Type	pdf
File Size	36.88 KB
Language	English
Subjects	-
Unlimited	MYR 0.00
Total read	-
URL	https://arxiv.org/abs/1504.05989

Citation

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AMA 11th EditionReferences

Mashkevich, Stefan. Statistics of two-dimensional random walks, the "cyclic sieving phenomenon" and the Hofstadter model. N.A. April 22, 2015. Accessed October 03, 2025. https://online.provdatabase.com/cite/18529

APA 7th EditionReferences

Mashkevich, Stefan. (2015). Statistics of two-dimensional random walks, the "cyclic sieving phenomenon" and the Hofstadter model. N.A. https://online.provdatabase.com/cite/18529

Chicago 17th EditionReferences

Mashkevich, Stefan. Statistics of two-dimensional random walks, the "cyclic sieving phenomenon" and the Hofstadter model. N.A. 2015. https://online.provdatabase.com/cite/18529

HarvardReferences

Mashkevich, Stefan. (2015). Statistics of two-dimensional random walks, the "cyclic sieving phenomenon" and the Hofstadter model. [Online]. N.A. Available from: https://online.provdatabase.com/cite/18529. (Accessed 03 October 2025).

Harvard AustraliaReferences

Mashkevich, Stefan, 2015, Statistics of two-dimensional random walks, the "cyclic sieving phenomenon" and the Hofstadter model, N.A, viewed 03 October 2025, <https://online.provdatabase.com/cite/18529>

MLA 9th EditionWorks Cited

Mashkevich, Stefan. Statistics of two-dimensional random walks, the "cyclic sieving phenomenon" and the Hofstadter model. N.A, 2015. PROV Database, https://online.provdatabase.com/cite/18529.

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