The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  • Benjamini, Itai; Häggström, Olle; Mossel, Elchanan. On random graph homomorphisms into ${\bf Z}$. J. Combin. Theory Ser. B 78 (2000), no. 1, 86--114. MR1737627
  • Benjamini, Itai; Peres, Yuval. Markov chains indexed by trees. Ann. Probab. 22 (1994), no. 1, 219--243. MR1258875
  • Benjamini, Itai; Peres, Yuval. Tree-indexed random walks on groups and first passage percolation. Probab. Theory Related Fields 98 (1994), no. 1, 91--112. MR1254826
  • Benjamini, Itai; Yadin, Ariel; Yehudayoff, Amir. Random graph-homomorphisms and logarithmic degree. Electron. J. Probab. 12 (2007), no. 32, 926--950. MR2324796
  • Brascamp, Herm Jan; Lieb, Elliot H.; Lebowitz, Joel L. The statistical mechanics of anharmonic lattices. Proceedings of the 40th Session of the International Statistical Institute (Warsaw, 1975), Vol. 1. Invited papers. Bull. Inst. Internat. Statist. 46 (1975), no. 1, 393--404 (1976). MR0676341
  • Erdös, Paul. On a lemma of Littlewood and Offord, Bull. Amer. Math. Soc. 51 (1945), 898--902.
  • Galvin, David. On homomorphisms from the Hamming cube to ${\bf Z}$. Israel J. Math. 138 (2003), 189--213. MR2031957
  • Kahn, Jeff. Range of cube-indexed random walk. Israel J. Math. 124 (2001), 189--201. MR1856513
  • Levin, David A.; Peres, Yuval; Wilmer, Elizabeth L. Markov chains and mixing times. With a chapter by James G. Propp and David B. Wilson. American Mathematical Society, Providence, RI, 2009. xviii+371 pp. ISBN: 978-0-8218-4739-8 MR2466937
  • Peled, Ron. High-dimensional Lipschitz functions are typically flat, arXiv preprint arXiv:1005.4636, To appear in Annals of Probability (2010).
  • Peled, Ron; Samotij, Wojciech; Yehudayoff, Amir. Lipschitz functions on expanders are typically flat. Combin. Probab. Comput. 22 (2013), no. 4, 566--591. MR3073490
  • Propp, James Gary; Wilson, David Bruce. Exact sampling with coupled Markov chains and applications to statistical mechanics. Proceedings of the Seventh International Conference on Random Structures and Algorithms (Atlanta, GA, 1995). Random Structures Algorithms 9 (1996), no. 1-2, 223--252. MR1611693


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.