Couplings of uniform spanning forests
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- Proc. Amer. Math. Soc. 132 (2004), 2151-2158 Request permission
Abstract:
We prove the existence of an automorphism-invariant coupling for the wired and the free uniform spanning forests on connected graphs with residually amenable automorphism groups.References
- Itai Benjamini, Russell Lyons, Yuval Peres, and Oded Schramm, Uniform spanning forests, Ann. Probab. 29 (2001), no. 1, 1–65. MR 1825141, DOI 10.1214/aop/1008956321
- Mohammed E. B. Bekka and Alain Valette, Group cohomology, harmonic functions and the first $L^2$-Betti number, Potential Anal. 6 (1997), no. 4, 313–326. MR 1452785, DOI 10.1023/A:1017974406074
- T. Feder and M. Mihail, Balanced Matroids, Proc. 24th Annual ACM Sympos. Theory Computing (Victoria, BC, Canada), pp. 26-38, ACM Press, New York, 1992.
- Russell Lyons, A bird’s-eye view of uniform spanning trees and forests, Microsurveys in discrete probability (Princeton, NJ, 1997) DIMACS Ser. Discrete Math. Theoret. Comput. Sci., vol. 41, Amer. Math. Soc., Providence, RI, 1998, pp. 135–162. MR 1630412
- R. Lyons, Determinantal Probability Measures, preprint.
- Ilya Kapovich and Daniel T. Wise, The equivalence of some residual properties of word-hyperbolic groups, J. Algebra 223 (2000), no. 2, 562–583. MR 1735163, DOI 10.1006/jabr.1999.8104
- Leonard Eugene Dickson, New First Course in the Theory of Equations, John Wiley & Sons, Inc., New York, 1939. MR 0000002
- A. Yu. Ol′shanskiĭ, Almost every group is hyperbolic, Internat. J. Algebra Comput. 2 (1992), no. 1, 1–17. MR 1167524, DOI 10.1142/S0218196792000025
- Robin Pemantle, Choosing a spanning tree for the integer lattice uniformly, Ann. Probab. 19 (1991), no. 4, 1559–1574. MR 1127715
- Jean-Paul Pier, Amenable locally compact groups, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1984. A Wiley-Interscience Publication. MR 767264
- E. A. Scott, A tour around finitely presented infinite simple groups, Algorithms and classification in combinatorial group theory (Berkeley, CA, 1989) Math. Sci. Res. Inst. Publ., vol. 23, Springer, New York, 1992, pp. 83–119. MR 1230630, DOI 10.1007/978-1-4613-9730-4_{4}
- V. Strassen, The existence of probability measures with given marginals, Ann. Math. Statist. 36 (1965), 423–439. MR 177430, DOI 10.1214/aoms/1177700153
- B. A. F. Wehrfritz, Infinite linear groups. An account of the group-theoretic properties of infinite groups of matrices, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 76, Springer-Verlag, New York-Heidelberg, 1973. MR 0335656
- Robert J. Zimmer, Ergodic theory and semisimple groups, Monographs in Mathematics, vol. 81, Birkhäuser Verlag, Basel, 1984. MR 776417, DOI 10.1007/978-1-4684-9488-4
Additional Information
- Lewis Bowen
- Affiliation: Department of Mathematics, University of California, Davis, California 95616
- MR Author ID: 671629
- Email: lbowen@math.ucdavis.edu
- Received by editor(s): January 30, 2003
- Received by editor(s) in revised form: April 14, 2003
- Published electronically: January 22, 2004
- Additional Notes: This research was supported in part by NSF Vigre Grant No. DMS-0135345
- Communicated by: Richard C. Bradley
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 2151-2158
- MSC (2000): Primary 60D05, 05C05, 60B99, 20F32
- DOI: https://doi.org/10.1090/S0002-9939-04-07304-6
- MathSciNet review: 2053989