We prove absence of infinite clusters and contours in a class of critical constrained percolation models on the square lattice. The percolation configuration is assumed to satisfy certain hard local constraints, but only weak symmetry and ergodicity conditions are imposed on its law. The proofs use new combinatorial techniques exploiting

We link conditional weak mixing and ergodicity via the tensor product in Riesz spaces. In particular, we characterise of a expectation preserving system by its with itself or other ergodic systems. Along way components order units space terms products units.

Quantum many-body scarring (QMBS) is a recently discovered form of weak ergodicity breaking in strongly interacting quantum systems, which presents opportunities for mitigating thermalization-induced decoherence information processing applications. However, the existing experimental realizations QMBS are based on systems with specific kinetic constrains. Here we experimentally realize distinct ...

The weak mean equicontinuity for a countable discrete amenable group G acting continuously on compact metrizable space X is studied. It shown that equicontinuity, pointwise ergodicity and uniformity are coincided. Moreover, we prove (X, G) equicontinuous if only the product system \((X \times X,G)\) equicontinuous.

We consider a weak form of controllability for system that have a conserved quantity and satisfy a condition of Hörmander type. It is shown that such systems are approximately controllable under a weak growth condition for the conserved quantity. The proof of the result combines analytic tools with probabilistic arguments. A counterexample is given that shows that the growth condition is essent...

Recent experiments on blinking quantum dots, weak turbulence in liquid crystals, and nanoelectrodes reveal the fundamental connection between 1/f noise and power law intermittency. The nonstationarity of the process implies that the power spectrum is random--a manifestation of weak ergodicity breaking. Here, we obtain the universal distribution of the power spectrum, which can be used to identi...

Abstract. We define a stronger property than unique ergodicity with respect to the fixed–point subalgebra firstly investigated in [1]. Such a property is denoted as F–strict weak mixing (F stands for the Markov projection onto the fixed–point operator system). Then we show that the free shifts on the reduced C–algebras of RD–groups, including the free group on infinitely many generators, and am...

We study the self-averaging properties and ergodicity of the mean square displacement m(t) of particles diffusing in d dimensional quenched random environments which give rise to subdiffusive average motion. These properties are investigated in terms of the sample to sample fluctuations as measured by the variance of m(t). We find that m(t) is not self-averaging for d<2 due to the inefficient d...

In this talk, I will extend Doeblin’s ergodicity coefficient (originally defined for finite dimensional stochastic matrices) to kernels of time-homogenous Markov chains over Polish spaces, and show how a strictly positive Doeblin’s coefficient leads to lowto moderatecomplexity approximations of the occupancy distributions of subsets of the state space. Such approximations may be particularly us...