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We prove that for some manifolds $M$ the set of robustly transitive partially hyperbolic diffeomorphisms of $M$ with one-dimensional nonhyperbolic centre direction contains a $C^1$-open and dense subset of diffeomorphisms with nonhyperbolic…
[GIKN] and [BBD1] propose two very different ways for building non hyperbolic measures, [GIKN] building such a measure as the limit of periodic measures and [BBD1] as the $\omega$-limit set of a single orbit, with a uniformly vanishing…
The dynamical properties and mechanical functions of amorphous materials are governed by their microscopic structures, particularly the elasticity of the interaction networks, which is generally complicated by structural heterogeneity. This…
We introduce a multivariate Hawkes process with constraints on its conditional density. It is a multivariate point process with conditional intensity similar to that of a multivariate Hawkes process but certain events are forbidden with…
In this paper, we investigate entanglement for causally connected subregions $A$ and $B$ in quantum field theory and holography. Recent developments have established that a transition operator $T_{AB}$ can be well-defined for such…
We develop a rotational hyperbolic theory for surface homeomorphisms. We use the equivalence relation on ergodic measures that have nontrivial rotational behaviour defined in [arXiv:2312.06249] to define a rotational counterpart of…
We study the ergodic properties of generic continuous dynamical systems on compact manifolds. As a main result we prove that generic homeomorphisms have convergent Birkhoff averages under continuous observables at Lebesgue almost every…
In this paper, we establish a new quasi-shadowing property for any nonuiformly partially hyperbolic set of a $C^{1+\alpha}$ diffeomorphism, which is adaptive to the movement of the pseudo-orbit. Moreover, the quasi-specification property…
Entanglement plays a prominent role in the study of condensed matter many-body systems: Entanglement measures not only quantify the possible use of these systems in quantum information protocols, but also shed light on their physics.…
The intricate relations between elements in natural and human-made systems sustain the complex processes that shape our world, forming multiscale networks of interactions. These networks can be represented as graphs composed of nodes…
We show that weak measurements can induce a quantum phase transition of interacting many-body systems from an ergodic thermal phase with a large entropy to a nonergodic localized phase with a small entropy, but only if the measurement…
The Rosenzweig-Porter model has seen a resurgence in interest as it exhibits a non-ergodic extended phase between the ergodic extended metallic phase and the localized phase. Such a phase is relevant to many physical models from the…
In this article we prove that for a $C^{1+\alpha}$ diffeomorphism on a compact Riemannian manifold, if there is a hyperbolic ergodic measure whose support is not uniformly hyperbolic, then the topological entropy of the set of irregular…
In this paper we discuss how the notion of subgeometric ergodicity in Markov chain theory can be exploited to study stationarity and ergodicity of nonlinear time series models. Subgeometric ergodicity means that the transition probability…
In this paper we prove the following result, useful and often needed in the study of the ergodic properties of hard ball systems: In any such system, for any phase point x with a non-singular forward trajectory and infinitely many connected…
Despite being governed by the familiar laws of Hookean mechanics, elastic shells patterned with an internal structure (i.e. metashells) exhibit a wealth of unusual mechanical properties with no counterparts in unstructured materials. Here I…
A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…
The use of higher-order stochastic processes such as nonlinear Markov chains or vertex-reinforced random walks is significantly growing in recent years as they are much better at modeling high dimensional data and nonlinear dynamics in…
Consider a subshift over a finite alphabet, $X\subset \Lambda^{\mathbb Z}$ (or $X\subset\Lambda^{\mathbb N_0}$). With each finite block $B\in\Lambda^k$ appearing in $X$ we associate the empirical measure ascribing to every block…
The entanglement entropy (EE) can measure the entanglement between a spatial subregion and its complement, which provides key information about quantum states. Here, rather than focusing on specific regions, we study how the entanglement…