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Volumn 13, Issue 3, 2003, Pages 817-844

Information flow on trees

Author keywords

Census; Information flow; Markov random field; Reconstruction problem; Reed Solomon codes; Second eigenvalue; Secret sharing; Thompson's principle; Tree index Markov chain

Indexed keywords


EID: 1842550501     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1060202828     Document Type: Article
Times cited : (127)

References (28)
  • 2
    • 21844521007 scopus 로고
    • On the purity of limiting Gibbs state for the Ising model on the Bethe lattice
    • BLEHER, P. M., RUIZ, J. and ZAGREBNOV, V. A. (1995). On the purity of limiting Gibbs state for the Ising model on the Bethe lattice. J. Statist. Phys. 79 473-482.
    • (1995) J. Statist. Phys. , vol.79 , pp. 473-482
    • Bleher, P.M.1    Ruiz, J.2    Zagrebnov, V.A.3
  • 3
    • 0000700530 scopus 로고    scopus 로고
    • Graph homomorphisms and phase transitions
    • BRIGHTWELL, G. and WINKLER, P. (1999). Graph homomorphisms and phase transitions. J. Combin. Theory Ser. B 77 415-435.
    • (1999) J. Combin. Theory Ser. B , vol.77 , pp. 415-435
    • Brightwell, G.1    Winkler, P.2
  • 6
    • 0018002532 scopus 로고
    • Taxonomy with confidence
    • CAVENDER, J. (1978). Taxonomy with confidence. Math. Biosci. 40 271-280.
    • (1978) Math. Biosci. , vol.40 , pp. 271-280
    • Cavender, J.1
  • 11
    • 84959747425 scopus 로고
    • Toward defining the course of evolution: Minimum change for a specific tree topology
    • FITCH, W. M. (1971). Toward defining the course of evolution: Minimum change for a specific tree topology. Systematic Zoology 20 406-416.
    • (1971) Systematic Zoology , vol.20 , pp. 406-416
    • Fitch, W.M.1
  • 12
    • 0026121386 scopus 로고
    • On the maximum tolerable noise for reliable computation by formulas
    • HAJEK, B. and WELLER, T. (1991). On the maximum tolerable noise for reliable computation by formulas. IEEE Trans. Inform. Theory 37 388-391.
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 388-391
    • Hajek, B.1    Weller, T.2
  • 13
    • 0007226988 scopus 로고
    • Remarks on the limiting Gibbs state on a (d + 1)-tree
    • HIGUCHI, Y. (1977). Remarks on the limiting Gibbs state on a (d + 1)-tree. Publ. RIMS Kyoto Univ. 13 335-348.
    • (1977) Publ. RIMS Kyoto Univ. , vol.13 , pp. 335-348
    • Higuchi, Y.1
  • 14
    • 0000572082 scopus 로고    scopus 로고
    • A note on the extremality of the disordered state for the Ising model on the Bethe lattice
    • IOFFE, D. (1996). A note on the extremality of the disordered state for the Ising model on the Bethe lattice. Lett. Math. Phys. 37 137-143.
    • (1996) Lett. Math. Phys. , vol.37 , pp. 137-143
    • Ioffe, D.1
  • 15
    • 0038871734 scopus 로고    scopus 로고
    • A note on the extremality of the disordered state for the Ising model on the Bethe lattice
    • (B. Chauvin, S. Cohen and A. Rouait, eds,). Birkhäuser, Boston
    • IOFFE, D. (1996). A note on the extremality of the disordered state for the Ising model on the Bethe lattice. In Trees (B. Chauvin, S. Cohen and A. Rouait, eds,). Birkhäuser, Boston.
    • (1996) Trees
    • Ioffe, D.1
  • 16
    • 0035176101 scopus 로고    scopus 로고
    • Glauber dynamics on trees and hyperbolic graphs
    • To appear
    • KENYON, C., MOSSEL, E. and PERES, Y. (2001). Glauber dynamics on trees and hyperbolic graphs (extended abstract). In Proceedings of FOCS 2001. To appear.
    • (2001) Proceedings of FOCS 2001
    • Kenyon, C.1    Mossel, E.2    Peres, Y.3
  • 17
    • 0001552596 scopus 로고
    • Limit theorems for decomposable multidimensional Galton-Watson processes
    • KESTEN, H. and STIGUM, B. P. (1966). Limit theorems for decomposable multidimensional Galton-Watson processes. J. Math. Anal. Appl. 17 309-338.
    • (1966) J. Math. Anal. Appl. , vol.17 , pp. 309-338
    • Kesten, H.1    Stigum, B.P.2
  • 18
    • 0002610091 scopus 로고
    • Additional limit theorem for indecomposable multidimensional Galton-Watson processes
    • KESTEN, H. and STIGUM, B. P. (1966). Additional limit theorem for indecomposable multidimensional Galton-Watson processes. Ann. Math. Statist. 37 1463-1481.
    • (1966) Ann. Math. Statist. , vol.37 , pp. 1463-1481
    • Kesten, H.1    Stigum, B.P.2
  • 20
    • 0000902270 scopus 로고
    • Random walks and percolation on trees
    • LYONS, R. (1990). Random walks and percolation on trees. Ann. Probab. 18 931-958.
    • (1990) Ann. Probab. , vol.18 , pp. 931-958
    • Lyons, R.1
  • 21
    • 0000600594 scopus 로고
    • Random walk in a random environment and first-passage percolation on trees
    • LYONS, R. and PEMANTLE, R. (1992). Random walk in a random environment and first-passage percolation on trees. Ann. Probab. 20 125-136.
    • (1992) Ann. Probab. , vol.20 , pp. 125-136
    • Lyons, R.1    Pemantle, R.2
  • 22
    • 0032363381 scopus 로고    scopus 로고
    • Recursive reconstruction on periodic trees
    • MOSSEL, E. (1998). Recursive reconstruction on periodic trees. Random Structures Algorithms 13 81-97.
    • (1998) Random Structures Algorithms , vol.13 , pp. 81-97
    • Mossel, E.1
  • 23
    • 0035638147 scopus 로고    scopus 로고
    • Reconstruction on trees: Beating the second eigenvalue
    • MOSSEL, E. (2001). Reconstruction on trees: Beating the second eigenvalue. Ann, Appl. Probab. 11 285-300.
    • (2001) Ann, Appl. Probab. , vol.11 , pp. 285-300
    • Mossel, E.1
  • 24
    • 0033456088 scopus 로고    scopus 로고
    • Robust phase transitions for Heisenberg and other models on general trees
    • PEMANTLE, R. and STEIF, J. E. (1999). Robust phase transitions for Heisenberg and other models on general trees. Ann. Probab. 27 876-912.
    • (1999) Ann. Probab. , vol.27 , pp. 876-912
    • Pemantle, R.1    Steif, J.E.2
  • 25
    • 9144245836 scopus 로고
    • A class of multiple-error-correcting codes and the decoding scheme
    • REED, I. S. and SOLOMON, G. (1954). A class of multiple-error-correcting codes and the decoding scheme. IEEE Trans. Inform. Theory 4 38-49.
    • (1954) IEEE Trans. Inform. Theory , vol.4 , pp. 38-49
    • Reed, I.S.1    Solomon, G.2
  • 26
    • 0018545449 scopus 로고
    • How to share a secret?
    • SHAMIR, A. (1979). How to share a secret? Comm. ACM 22 612-613.
    • (1979) Comm. ACM , vol.22 , pp. 612-613
    • Shamir, A.1
  • 27
    • 0000318254 scopus 로고
    • Markov random fields on an infinite tree
    • SPITZER, F. (1975). Markov random fields on an infinite tree. Ann. Probab. 3 387-394.
    • (1975) Ann. Probab. , vol.3 , pp. 387-394
    • Spitzer, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.