Concentration for self-bounding functions and an inequality of talagrand

Random Structures and Algorithms

Volumn 29, Issue 4, 2006, Pages 549-557

  McDiarmid, Colin ^a   Reed, Bruce ^b,c  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b MCGILL UNIVERSITY   (Canada)

^c Institut de Geodynamique   (France)

Author keywords

Certificate; Concentration; Independent random variables; Self bounding function; Talagrand

Indexed keywords

EID: 33751501496     PISSN: 10429832     EISSN: 10982418     Source Type: Journal    
DOI: 10.1002/rsa.20145     Document Type: Article

References (15)

1. S. Boucheron, G. Lugosi, and P. Massart, A sharp concentration inequality with applications, Random Struct Algor 16 (2000), 277-292.
2. S. Boucheron, G. Lugosi, and P. Massait, Concentration inequalities using the entropy method, AnnProbab 31 (2003), 1583-1614.
3. L. Devroye, Laws of large numbers and tail inequalities for random tries and Patricia trees, J Computat Appl Math 142 (2002), 27-37.
4. R. Durrett, Probability: Theory and Examples, 2nd ed., Duxbury Press, 1996.
5. M. Ledoux, On Talagrand's deviation inequalities for product measures, ESIAM Probab Stat 1 (1997), 63-87.
6. M. Ledoux, The concentration of measure phenomenon, American Mathematical Society, Providence, RI, 2001.
7. G. Lugosi, Concentration-of-measure inequalities, lecture notes, 2004.
8. P. Massait, About the constants in Talagrand's concentration inequalities for empirical processes, Ann Probab 28 (2000), 863-884.
9. A. Maurer, Concentration inequalities for functions of independent variables, Random Struct Algor 29 (2006), 121-138.
10. C. McDiarmid, "On the method of bounded differences," Surveys in Combinatorics, J. Siemens (Editor), London Mathematical Society Lecture Note Series 141, Cambridge University Press, 1989.
11. C. McDiarmid, "Concentration," Probabilistic Methods for Algorithmic Discrete Mathematics, M. Habib, C. McDiarmid, J. Ramirez, and B. Reed (Editors), Springer-Verlag, 1998.
12. M. Molloy and B. Reed, Graph Colouring and the Probabilistic Method, Springer, 2002.
13. M. Steele, Probability Theory and Combinatorial Optimization, 1996.
14. M. Talagrand, Concentration of measure and isoperimetric inequalities in product spaces, Publ Math Inst Hautes Étud Sci 81 (1995), 73-205.
15. M. Talagrand, New concentration inequalities in product spaces, Invent Math 126 (1996), 505-563.