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Classical ergodic theory for integer-group actions uses entropy as a complete invariant for isomorphism of IID (independent, identically distributed) processes (a.k.a.
A new metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces
Kolmogorov, A.N · 1958
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Symmetric random walks on groups
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Entropy per unit time as a metric invariant of automorphisms
Kolmogorov, A.N · 1959
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On the concept of entropy for a dynamic system
Sinaĭ, Ja · 1959
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The structure and properties of invariant measurable partitions
Rohlin, V.A · 1961
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Bernoulli shifts with the same entropy are isomorphic
Ornstein, D.S · 1970
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Factors of Bernoulli shifts are Bernoulli shifts
Ornstein, D.S · 1970
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A partition on a Bernoulli shift which is not weakly Bernoulli
Smorodinsky, M · 1971
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An example of a Kolmogorov automorphism that is not a Bernoulli shift
Ornstein, D.S · 1973
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Ergodic Theory, Randomness, and Dynamical Systems
Ornstein, D.S · 1974
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Every transformation is bilaterally deterministic
Ornstein, D.S · 1974
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Poisson splitting by factors
Holroyd, A.E., Lyons, R., · 1982
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T , T − 1 T,\,T^{-1} transformation is not loosely Bernoulli
Kalikow, S.A · 1982
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Entropy and isomorphism theorems for actions of amenable groups
Ornstein, D.S · 1987
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The isoperimetric number of random regular graphs
Bollobás, B · 1988
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Very weak Bernoulli for amenable groups
Adams, S · 1992
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Automorphism invariant measures on trees
Pemantle, R · 1992
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Finite state bilaterally deterministic strongly mixing processes
Burton, R.M., Denker, M., · 1996
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On the edge-expansion of graphs
Alon, N · 1997
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Coupling surfaces and weak Bernoulli in one and higher dimensions
Burton, R.M · 1997
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Broadcasting on trees and the Ising model
Evans, W., Kenyon, C., Peres, Y., · 2000
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Upper bounds on the bisection width of 3- and 4-regular graphs
Monien, B · 2001
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Bounds on the max and min bisection of random cubic and random 4-regular graphs
Díaz, J., Do, N., Serna, M.J., · 2003
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Trees and matchings from point processes
Holroyd, A.E · 2003
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Tree and grid factors for general point processes
A factor of i.i.d with uniform marginals and infinite clusters spanned by equal labels
Mester, P · 2011
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Invariant colorings of random planar maps
Timár, Á · 2011
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Stationary map coloring
Angel, O., Benjamini, I., Gurel-Gurevich, O., Meyerovitch, T., · 2012
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Invariant random matchings in Cayley graphs
Csóka, E · 2012
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Maximum edge-cuts in cubic graphs with large girth and in random cubic graphs
Kardoš, F., Král’, D., · 2012
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Bernoulli actions are weakly contained in any free action
Abért, M · 2013
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Timár, Á · 2004
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Some computations of 1-cohomology groups and construction of non-orbit-equivalent actions
Popa, S · 2006
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Bounds on the bisection width for random d d -regular graphs
Díaz, J., Serna, M.J., · 2007
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Poisson matching
Holroyd, A.E., Pemantle, R., Peres, Y., · 2009
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Personal communication
Sly, A · 2009
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A measure-conjugacy invariant for free group actions
Bowen, L.P · 2010
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Personal communication
Bowen, L.P · 2013
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Brooks’ theorem for Bernoulli shifts
Conley, C.T · 2013
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Limits of local algorithms over sparse random graphs
Gamarnik, D · 2013
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Poisson thickening
Gurel-Gurevich, O · 2013
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Expanders have a spanning Lipschitz subgraph with large girth
Kun, G · 2013
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Fixed price of groups and percolation
Lyons, R · 2013
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Ramanujan graphings and correlation decay in local algorithms
Backhausz, Á., Szegedy, B., · 2015
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Invariant Gaussian processes and independent sets on regular graphs of large girth
Csóka, E., Gerencsér, B., Harangi, V., · 2015
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Extremal cuts of sparse random graphs
Dembo, A., Montanari, A., · 2015
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Independence ratio and random eigenvectors in transitive graphs
Harangi, V · 2015
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A monotone Sinai theorem
Quas, A · 2016
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