GRAPH LIMITS AND EXCHANGEABLE RANDOM

We develop a clear connection between deFinetti’s theorem for exchangeable arrays (work of Aldous–Hoover–Kallenberg) and the emerging area of graph limits (work of Lovász and many coauthors). Along the way, we translate the graph theory into more classical prob-

[1]  László Lovász,et al.  Contractors and connectors of graph algebras , 2005, J. Graph Theory.

[2]  B. Szegedy,et al.  Testing properties of graphs and functions , 2008, 0803.1248.

[3]  Svante Janson,et al.  Threshold Graph Limits and Random Threshold Graphs , 2008, Internet Math..

[4]  László Lovász,et al.  Generalized quasirandom graphs , 2008, J. Comb. Theory, Ser. B.

[5]  B. Szegedy,et al.  Szemerédi’s Lemma for the Analyst , 2007 .

[6]  V. Sós,et al.  Convergent Sequences of Dense Graphs I: Subgraph Frequencies, Metric Properties and Testing , 2007, math/0702004.

[7]  B. Bollobás,et al.  The phase transition in inhomogeneous random graphs , 2005, Random Struct. Algorithms.

[8]  László Lovász,et al.  Graph limits and parameter testing , 2006, STOC '06.

[9]  V. Sós,et al.  Counting Graph Homomorphisms , 2006 .

[10]  László Lovász,et al.  The rank of connection matrices and the dimension of graph algebras , 2004, Eur. J. Comb..

[11]  László Lovász,et al.  Limits of dense graph sequences , 2004, J. Comb. Theory B.

[12]  O. Kallenberg.  Probabilistic Symmetries and Invariance Principles , 2005 .

[13]  László Lovász.  Connection matrices , 2005 .

[14]  L. Lovasz,et al.  Reflection positivity, rank connectivity, and homomorphism of graphs , 2004, math/0404468.

[15]  D. Aldous.  Representations for partially exchangeable arrays of random variables , 1981 .

[16]  D. Freedman,et al.  On the statistics of vision: The Julesz conjecture☆ , 1981 .