Related papers: Random products of maps synchronizing on average
For any continuous self-map of a compact metric space, we provide sufficient conditions under which the infinite direct product of the map is $\omega$-chaotic. We also apply the result to obtain some examples of unusual $\omega$-chaotic…
For a product of i.i.d. random maps or a memoryless stochastic flow on a compact space $X$, we find conditions under which the presence of locally asymptotically stable trajectories (e.g. as given by negative Lyapunov exponents) implies…
An equivalent condition for the product of elements of an independent random sample on a compact algebraic group converging in distribution to some random variable as the sample size increases is obtained. Namely, a limit distribution…
We study independent and identically distributed random iterations of continuous maps defined on a connected closed subset $S$ of the Euclidean space $\mathbb{R}^{k}$. We assume the maps are monotone (with respect to a suitable partial…
In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.
Reflecting boundary conditions cause two one-dimensional random walks to synchronize if a common direction is chosen in each step. The mean synchronization time and its standard deviation are calculated analytically. Both quantities are…
A compactness of the Revuz map is established in the sense that the locally uniform convergence of a sequence of positive continuous additive functionals is derived in terms of their smooth measures. To this end, we first introduce a metric…
Synchronization of identical chaotic systems subjected to common noise has been the subject of recent research. Studies on several chaotic systems have shown that, the synchronization is actually induced by the non-zero mean of the noise,…
We show that the synchronized states of two systems of identical chaotic maps subject to either, a common drive that acts with a probability p in time or to the same drive acting on a fraction p of the maps, are similar. The synchronization…
We treat synchronization for iterated function systems generated by diffeomorphisms on compact manifolds. Synchronization here means the convergence of orbits starting at different initial conditions when iterated by the same sequence of…
We present a construction of a compact connected space which supports a normal probability measure.
A necessary and sufficient condition for a random walk in a finite directed graph subject to a road coloring to be measurable with respect to the driving random road colors is proved to be that the road coloring is synchronizing. For this,…
If we consider a sequence of warped product length spaces, what conditions on the sequence of warping functions implies compactness of the sequence of distance functions? In particular, we want to know when a subsequence converges to a well…
We investigate the spatiotemporal dynamics of a network of coupled chaotic maps, with varying degrees of randomness in coupling connections. While strictly nearest neighbour coupling never allows spatiotemporal synchronization in our…
On the plane, every random compact set with almost surely uncountable first projection intersects with a high probability the graph of some continuous function. Implication: every black noise over the plane fails to factorize when the plane…
We study Markovian random products on a large class of "m-dimensional" connected compact metric spaces (including products of closed intervals and trees). We introduce a splitting condition, generalizing the classical one by Dubins and…
We prove a sufficient condition for synchronization for coupled one-dimensional maps and estimate the size of the window of parameters where synchronization takes place. It is shown that coupled systems on graphs with positive eigenvalues…
We introduce and study systems of randomly coupled maps (RCM) where the relevant parameter is the degree of connectivity in the system. Global (almost-) synchronized states are found (equivalent to the synchronization observed in globally…
We give a geometric condition on a compact subset of a complex manifold which is necessary and sufficient for the existence of a smooth strictly plurisubharmonic function defined in a neighbourhood of this set.
We give conditions under which a product of topological spaces satisfies some local property. The conditions are necessary and sufficient when the corresponding global property is preserved under finite products. Further examples include…