| 1. |
- Johansson, Anders, et al.
(författare)
-
Countable state shifts and uniqueness of g-measures
- 2007
-
Ingår i: American Journal of Mathematics. - : Project Muse. - 0002-9327 .- 1080-6377. ; 129:6, s. 1501-1511
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper we present a new approach to studying g-measures which is based upon local absolute continuity. We extend an earlier result that square summability of variations of g ensures uniqueness of g-measures. The first extension is to the case of countably many symbols. The second extension is to some cases where g >= 0, relaxing the earlier requirement that inf g > 0.
|
|
| 2. |
- Johansson, Anders, 1960-, et al.
(författare)
-
Ergodic Theory of Kusuoka Measures
- 2017
-
Ingår i: Journal of Fractal Geometry. - : European Mathematical Society Publishing House. - 2308-1309 .- 2308-1317. ; 4:2, s. 185-214
-
Tidskriftsartikel (refereegranskat)abstract
- In the analysis on self-similar fractal sets, the Kusuoka measure plays an important role. Here we investigate the Kusuoka measure from an ergodic theoretic viewpoint, seen as an invariant measure on a symbolic space. Our investigation shows that the Kusuoka measure generalizes Bernoulli measures and their properties to higher dimensions of an underlying finite dimensional vector space. Our main result is that the transfer operator on functions has a spectral gap when restricted to a certain Banach space that contains the Hölder continuous functions, as well as the highly discontinuous g" role="presentation">g-function associated to the Kusuoka measure. As a consequence, we obtain exponential decay of correlations. In addition, we provide some explicit rates of convergence for a family of generalized Sierpinski gaskets.
|
|
| 3. |
- Johansson, Anders, 1960-, et al.
(författare)
-
Multifractal analysis of non-uniformly hyperbolic systems
- 2010
-
Ingår i: Israel Journal of Mathematics. - : Springer. - 0021-2172 .- 1565-8511. ; 177:1, s. 125-144
-
Tidskriftsartikel (refereegranskat)abstract
- We prove a multifractal formalismfor Birkhoff averages of continuous functions in the case of some non-uniformly hyperbolic maps, which includes interval examples such as the Manneville-Pomeau map.
|
|
| 4. |
- Johansson, Anders, 1960-, et al.
(författare)
-
Phase transitions in long-range Ising models and an optimal condition for factors of g-measures
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We weaken the assumption of summable variations in a paper by Verbitskiy \cite{verb} to a weaker condition, Berbee's condition, in order for a 1-block factor (a single site renormalisation) of the full shift space on finitely many symbols to have a $g$-measure with a continuous $g$-function. But we also prove by means of a counterexample, that this condition is (within constants) optimal. The counterexample is based on the second of our main results, where we prove that there is an inverse critical temperature in a one-sided long-range Ising model which is at most 8 times the critical inverse temperature for the (two-sided) Ising model with long-range interactions.
|
|
| 5. |
- Johansson, Anders, 1960-, et al.
(författare)
-
Phase transitions in long-range Ising models and an optimal condition for factors of g-measures
- 2019
-
Ingår i: Ergodic Theory and Dynamical Systems. - : Cambridge University Press. - 0143-3857 .- 1469-4417. ; 39:5, s. 1317-1330
-
Tidskriftsartikel (refereegranskat)abstract
- We weaken the assumption of summable variations in a paper by Verbitskiy [On factors of g-measures. Indag. Math. (N.S.) 22 (2011), 315-329] to a weaker condition, Berbee's condition, in order for a one-block factor (a single-site renormalization) of the full shift space on finitely many symbols to have a g-measure with a continuous g-function. But we also prove by means of a counterexample that this condition is (within constants) optimal. The counterexample is based on the second of our main results, where we prove that there is a critical inverse temperature in a one-sided long-range Ising model which is at most eight times the critical inverse temperature for the (two-sided) Ising model with long-range interactions.
|
|
| 6. |
- Johansson, Anders, 1960-, et al.
(författare)
-
Unique Bernoulli g-measures
- 2012
-
Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society Publishing House. - 1435-9855 .- 1435-9863. ; 14:5, s. 1599-1615
-
Tidskriftsartikel (refereegranskat)abstract
- We improve and subsume the conditions of Johansson and O¨ berg [18] and Berbee [2]for uniqueness of a g-measure, i.e., a stationary distribution for chains with complete connections.In addition, we prove that these unique g-measures have Bernoulli natural extensions. In particular,we obtain a unique g-measure that has the Bernoulli property for the full shift on finitely manystates under any one of the following additional assumptions.(1)P1n=1(varn log g)2 < 1,(2) For any fixed ✏ > 0,P1n=1 e−(1/2+✏)(var1 log g+···+varn log g) = 1,(3) varn log g = o(1/pn) as n!1.That the measure is Bernoulli in the case of (1) is new. In (2) we have an improved version ofBerbee’s [2] condition (concerning uniqueness and Bernoullicity), allowing the variations of log gto be essentially twice as large. Finally, (3) is an example that our main result is new both foruniqueness and for the Bernoulli property.We also conclude that we have convergence in the Wasserstein metric of the iterates of theadjoint transfer operator to the g-measure.
|
|
