The Poisson Boundary of Polycyclic Groups

Vadim A. Kaimanovich

Publications mathématiques et informatique de Rennes (1994)

  • Issue: 2, page 1-14

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Kaimanovich, Vadim A.. "The Poisson Boundary of Polycyclic Groups." Publications mathématiques et informatique de Rennes (1994): 1-14. <http://eudml.org/doc/274851>.

@article{Kaimanovich1994,
author = {Kaimanovich, Vadim A.},
journal = {Publications mathématiques et informatique de Rennes},
keywords = {Poisson boundary for measures; polycyclic groups; Lie group},
language = {eng},
number = {2},
pages = {1-14},
publisher = {Département de Mathématiques et Informatique, Université de Rennes},
title = {The Poisson Boundary of Polycyclic Groups},
url = {http://eudml.org/doc/274851},
year = {1994},
}

TY - JOUR
AU - Kaimanovich, Vadim A.
TI - The Poisson Boundary of Polycyclic Groups
JO - Publications mathématiques et informatique de Rennes
PY - 1994
PB - Département de Mathématiques et Informatique, Université de Rennes
IS - 2
SP - 1
EP - 14
LA - eng
KW - Poisson boundary for measures; polycyclic groups; Lie group
UR - http://eudml.org/doc/274851
ER -

References

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  2. 2. L. Auslander, "An exposition of the structure of solvmanifolds", Bull Amer. Math. Soc.79 (1973), 227-285. Zbl0265.22016MR486307
  3. 3. R. Azencott, Espaces de Poisson des groupes localement compacts, (Springer, Berlin, 1970, Lecture Notes in Math.148). Zbl0208.15302MR501376
  4. 4. H. Furstenberg, "A Poisson formula for semi-simple Lie groups", Ann. of Math.77 (1963), 335-386. Zbl0192.12704MR146298
  5. 5. R. W. Goodman, Nilpotent Lie Groups (Springer, Berlin, 1976, Lecture Notes in Math.562). Zbl0347.22001MR442149
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  7. 7. V. A. Kaimanovich, "Brownian motion and harmonic functions on covering manifolds. An entropy approach", Soviet Math. Dokl.33 (1986), 812-816. Zbl0615.60074MR852647
  8. 8. V. A. Kaimanovich, "Boundaries of random walks on polycyclic groups and the law of large numbers for solvable Lie groups", Vestnik Leningrad University: Mathematics20:4 (1987), 49-52. Zbl0631.60006MR931055
  9. 9. V. A. Kaimanovich, "Poisson boundaries of random walks on discrete solvable groups", in Probability Measures on Groups X , ed. H. Heyer (Plenum, New York, 1991), 205-238. Zbl0823.60006MR1178986
  10. 10. V. A. Kaimanovich, "The Poisson boundary of hyperbolic groups", C.R. Ac. Sci.Paris318 (1994), 59-64. Zbl0792.60006MR1260536
  11. 11. V. A. Kaimanovich, "An introduction to boundary theory of invariant Markov operators", in Proceedings of the Conference on Algebraic and Number Theoretic Aspects of Ergodic Theory (Warwick, 1994), to appear. 
  12. 12. V. A. Kaimanovich and A. M. Vershik, "Random walks on discrete groups: boundary and entropy", Ann. Prob.11 (1983), 457-490. Zbl0641.60009MR704539
  13. 13. F. Ledrappier, "Poisson boundaries of discrete groups of matrices", Israel J. Math.50 (1985), 319-336. Zbl0574.60012MR800190
  14. 14. T. Lyons, "Random thoughts on reversible potential theory", in Summer School on Potential Theory (Joensuu, 1990), ed. Ilpo Laine (Joensuu Publ. in Sciences26, 1992), 71-114. Zbl0757.31007MR1175217
  15. 15. T. Lyons and D. Sullivan, "Function theory, random paths and covering spaces", J. Diff. Geom., 19 (1984), 299-323. Zbl0554.58022MR755228
  16. 16. A. Raugi, "Fonctions harmoniques sur les groupes localement compacts à base dénombrable", Bull. Soc. Math. France. Mémoire 54 (1977), 5-118. Zbl0389.60003MR517392
  17. 17. D. Segal, Polycyclic groups (Cambridge University Press, 1983, Cambridge Tracts in Math.82). Zbl0516.20001MR713786

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