Exact solution for statics and dynamics of maximal-entropy random walks on Cayley trees

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 85, Issue 2, 2012, Pages

  Ochab, J K ^a   Burda, Z ^a  

^a JAGIELLONIAN UNIVERSITY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

ADJACENCY MATRICES; ANALYTICAL SOLUTIONS; CAYLEY TREES; EIGENVALUES; EXACT SOLUTION; INITIAL CONDITIONS; LARGEST EIGENVALUES; RANDOM WALK; SECOND LARGEST EIGENVALUE; STATIONARY STATE; SYSTEM SIZE; TREE STRUCTURES;

DYNAMICS; ENTROPY; FORESTRY; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES; TREES (MATHEMATICS);

EIGENVALUES AND EIGENFUNCTIONS;

ENTROPY; FORESTRY; MATRICES; PROBABILITY; RANDOM PROCESSES; RELAXATION;

EID: 84857726509     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.85.021145     Document Type: Article

References (20)

1. A. Einstein, Ann. Phys. (Leipzig) 0003-3804 10.1002/andp.19053220806 322 (8), 549 (1905);
2. A. Einstein, Ann. Phys. (Leipzig) 10.1002/andp.19063240208 324 (2), 371 (1906).
3. M. Smoluchowski, Ann. Phys. (Leipzig) 0003-3804 10.1002/andp.19063261405 326 (14), 756 (1906).
4. G. Polya, Math. Ann. MAANA3 0025-5831 10.1007/BF01458701 84, 149 (1921).
5. Z. Burda, J. Duda, J. M. Luck, and B. Waclaw, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.160602 102, 160602 (2009).
6. Z. Burda, J. Duda, J. M. Luck, and B. Waclaw, Acta Phys. Pol. B 41, 949 (2010).
7. L. Demetrius, V. M. Gundlach, and G. Ochs, Theor. Popul. Biol. TLPBAQ 0040-5809 10.1016/j.tpb.2003.12.002 65, 211 (2004). (Pubitemid 38458857)
8. L. Demetrius and T. Manke, Physica A PHYADX 0378-4371 10.1016/j.physa.2004.07.011 346, 682 (2005).
9. J. H. Hetherington, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.30. 2713 30, 2713 (1984).
10. V. Zlatic, A. Gabrielli, and G. Caldarelli, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.066109 82, 066109 (2010).
11. J.-C. Delvenne and A.-S. Libert, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.046117 83, 046117 (2011).
12. R. Sinatra, J. Gomez-Gardenes, R. Lambiotte, Vincenzo Nicosia, and Vito Latora, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.030103 83, 030103 (2011).
13. C. Monthus and T. Garel, J. Phys. A 1751-8113 10.1088/1751-8113/44/8/ 085001 44, 085001 (2011).
14. K. Anand, G. Bianconi, and S. Severini, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.036109 83, 036109 (2011).
15. B. Waclaw, Generic Random Walk and Maximal-Entropy Random Walk, Wolfram Demonstration Project, http://demonstrations.wolfram.com/ GenericRandomWalkAndMaximalEntropyRandomWalk/.
16. W. M. X. Zimmer and G. M. Obermair, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/11/6/022 11, 1119 (1978).
17. W. Parry, Trans. Amer. Math. Soc. TAMTAM 0002-9947 10.1090/S0002-9947- 1964-0161372-1 112, 55 (1964).
18. J. K. Ochab, Stationary States of Maximal-Entropy Random Walk and Generic Random Walk on Cayley Trees, Wolfram Demonstration Project, http://demonstrations.wolfram.com/ StationaryStatesOfMaximalEntropyRandomWalkAndGenericRandomWa/.
19. J. K. Ochab, Dynamics of Maximal-Entropy Random Walk and Generic Random Walk on Cayley Trees, Wolfram Demonstration Project, http://demonstrations. wolfram.com/DynamicsOfMaximalEntropyRandomWalkAndGenericRandomWalkOnCayl/.
20. S. Fortunato, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2009.11.002 486, 75 (2010).