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pro vyhledávání: '"37a50"'
Autor:
Tsankov, Todor
We prove two theorems in the ergodic theory of infinite permutation groups. First, generalizing a theorem of Nessonov for the infinite symmetric group, we show that every non-singular action of a non-archimedean, Roelcke precompact, Polish group on a
Externí odkaz:
http://arxiv.org/abs/2411.04716
We establish a connection between percolation on the Cayley graphs of a group and the dynamical diversity of cellular automata on that group. Specifically, we demonstrate that Gilman's dichotomy between equicontinuity and sensitivity with respect to
Externí odkaz:
http://arxiv.org/abs/2410.23770
Autor:
Jahel, Colin, Perruchaud, Pierre
The classical de Finetti Theorem classifies the $\mathrm{Sym}(\mathbb N)$-invariant probability measures on $[0,1]^{\mathbb N}$. More precisely it states that those invariant measures are combinations of measures of the form $\nu^{\otimes\mathbb N}$
Externí odkaz:
http://arxiv.org/abs/2410.22930
We study random dynamical systems of certain continuous functions on the unit interval. We use bounded variation to provide sufficient conditions for unique ergodicity of these systems. Several classes of examples are provided.
Externí odkaz:
http://arxiv.org/abs/2410.18664
We study the asymptotic behaviour of stationary densities of one-dimensional random diffeomorphisms, at the boundaries of their support, which correspond to deterministic fixed points of extremal diffeomorphisms. In particular, we show how this stati
Externí odkaz:
http://arxiv.org/abs/2410.18554
This paper concerns discrete-time occupancy processes on a finite graph. Our results can be formulated in two theorems, which are stated for vertex processes, but also applied to edge process (e.g., dynamic random graphs). The first theorem shows tha
Externí odkaz:
http://arxiv.org/abs/2410.06807
We study the small noise asymptotic for stochastic Burgers equations on $(0,1)$ with Dirichlet boundary condition. We consider the case that the noise is more singular than space-time white noise. We let the noise magnitude $\sqrt{\epsilon} \rightarr
Externí odkaz:
http://arxiv.org/abs/2409.14234
Autor:
Kosloff, Zemer, Sanadhya, Shrey
We show that for every ergodic and aperiodic probability preserving system $(X,\mathcal{B},m,T)$, there exists $f:X\to \mathbb{Z}^d$, whose corresponding cocycle satisfies the $d$-dimensional local central limit theorem. We use the $2$-dimensional re
Externí odkaz:
http://arxiv.org/abs/2409.05087
Autor:
Das, Suddhasattwa
A discrete-time deterministic dynamical system is governed at every step by a predetermined law. However the dynamics can lead to many complexities in the phase space and in the domain of observables that makes it comparable to a stochastic process.
Externí odkaz:
http://arxiv.org/abs/2409.02318
Despite the huge number of research into the three-body problem in physics and mathematics, the study of this problem still remains relevant both from the point of view of its broad application and taking into account its fundamental significance for
Externí odkaz:
http://arxiv.org/abs/2408.13969