Eigenmodes of a random walk on a 2-D lattice torus with one trap

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The complete set of eigenvalues and eigenmodes is elaborated for a random walk on a two-dimensional N )times) N square lattice torus with one trap site. The eigenvalue closest to unity is found to have an asymptotic expansion in N; the leading behavior is lambda )approximately) 1 )minus) ..pi.. (2N/sup 2/ log N) )plus) O(N log N)/sup )minus/2). In general, the eigenvalues and eigenmodes for this problem are constructed from those for a random walk on the same lattice containing no trap. The degeneracy of the latter eigenmodes is a prominent feature of this construction, and a formula is derived ... continued below

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Pages: 15

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Torney, D.C. March 14, 1988.

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The complete set of eigenvalues and eigenmodes is elaborated for a random walk on a two-dimensional N )times) N square lattice torus with one trap site. The eigenvalue closest to unity is found to have an asymptotic expansion in N; the leading behavior is lambda )approximately) 1 )minus) ..pi.. (2N/sup 2/ log N) )plus) O(N log N)/sup )minus/2). In general, the eigenvalues and eigenmodes for this problem are constructed from those for a random walk on the same lattice containing no trap. The degeneracy of the latter eigenmodes is a prominent feature of this construction, and a formula is derived for this degeneracy. 9 refs., 2 figs

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Pages: 15

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  • Conference on transport theory, invariant imbedding and integral equations, Santa Fe, NM, USA, 20 Jan 1988

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  • Other: DE88007830
  • Report No.: LA-UR-88-915
  • Report No.: CONF-880123-2
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 5183034
  • Archival Resource Key: ark:/67531/metadc1058964

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  • March 14, 1988

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  • Jan. 22, 2018, 7:23 a.m.

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  • Feb. 1, 2018, 7:04 p.m.

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Torney, D.C. Eigenmodes of a random walk on a 2-D lattice torus with one trap, article, March 14, 1988; New Mexico. (digital.library.unt.edu/ark:/67531/metadc1058964/: accessed October 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.