Phase Transitions for Countable Markov Shifts

By O. Sarig. 2001

179 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ab72408f6d04b8150298e7e77b2f972111722d63

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Vilton Pinheiro
2. Jérôme Buzzi
3. Van Cyr
4. O. Sarig
5. Mike Boyle
6. Ricardo Gómez
7. T. Jordan
8. Mike Todd

In Statistical and Nonlinear Physics

1. Jérôme Buzzi
2. T. Jordan
3. Vilton Pinheiro
4. Mike Todd
5. Tuomas Sahlsten
6. Henk Bruin
7. G. Iommi
8. Sylvie Ruette

Citations in the corpus

• Expanding Measures (2008, background): “Future applications Recently there was an increasing development of the study of the thermodynamic formalism beyond the uniformly hyperbolic context (including countable Markov shift) by several authors (this list is certainly not complete): Araujo [7], Arbieto, Matheus, Oliveira, Varandas, Viana [8”
• Almost isomorphism for countable state Markov shifts (2004, background): “One motivation of our paper is recent interest in the thermodynamic formalism for countable state Markov shifts [11, 18, 23, 24, 25, 39, 49, 50, 51, 53].”
• On the Vere–Jones classification and existence of maximal measures for countable topological Markov chains (2003, background): “Examples of (non-null) potentials which are positive recurrent but not strongly positive recurrent can be found in [15]; some of them resemble much the Markov chains of Example 2.”
• Existence of gibbs measures for countable Markov shifts (2003, methodology): “1 The version which was proved in [12] used stronger continuity assumptions on φ, but the proof given there works verbatim in our context.”
• Existence, uniqueness and stability of equilibrium states for non-uniformly expanding maps (2008, unknown): “Buzzi, Sarig [BS03, Sar99, Sar01 , Sar03, Yur03] for countable Markov shifts.”
• Equilibrium States for Interval Maps: Potentials with sup φ − inf φ < htop(f) (2007, methodology): “Combining inducing schemes with ideas of so-called Hofbauer towers and infinite state Markov chains (as presented by Sarig [Sa1, Sa2, Sa3]), we proved the existence and uniqueness of equilibrium states within the class M + = { µ ∈ M erg : λ ( µ ) > 0 , supp( µ ) 6⊂ orb(Crit) } . where λ ( µ ) = log…”
• Uniqueness of equilibrium measures for countable Markov shifts and multidimensional piecewise expanding maps (2003, methodology): “We remark that this proof uses the generalized Ruelle’s Perron–Frobenius Theorem of [24, 25].”
• Fourier transforms of Gibbs measures for the Gauss map (2013, methodology): “It follows from Lemma 1 in [31] that if P (ψ) <∞ then we can find a locally Hölder φ such that φ ≤ 0, P (φ) = 0 , Lφ1 = 1 and φ− ψ is cohomologous to a constant in the class of bounded Hölder potentials.”
• Spectral Gap and Transience for Ruelle Operators on Countable Markov Shifts (2009, background): “Dene p a[ ] := supfp j PG( +p) S3 ]”
• Subexponential decay of correlations (2002, result): “So is log 1 (T ϕ )� , by an argument similar to [ S2 ] p. 564.”
• A multifractal formalism for growth rates and applications to geometrically finite Kleinian groups (2004, unknown): “[ADU93], [Byr98], [DU91], [Fri00a, Fri00b], [Hof77], [Nak00], [Pes97], [PW97], [PW99], [PS92], [ Sar01 ], [Smi96], [Wal78]).”
• Multifractal analysis of Birkhoff averages for countable Markov maps (2010, background): “The following proposition is a direct consequence of results by Mauldin and Urbański [23], Sarig [29] and Stratmann and Urbański [31].”