Related papers: From slightly coloured noises to unitless product …
An overdamped system with a linear restoring force and two multiplicative colored noises is considered. Noise amplitudes depend on the system state $x$ as $x$ and $|x|^{\alpha}$. An exactly soluble model of a system is constructed due to…
Score-based diffusion models generate samples from an unknown target distribution using a time-reversed diffusion process. While such models represent state-of-the-art approaches in industrial applications such as artificial image…
Continuous frames and tensor products are important topics in theoretical physics. This paper combines those concepts. We derive fundamental properties of continuous frames for tensor product of Hilbert spaces. This includes, for example,…
We develop a representative-level framework for the Liebscher-Tsirelson random-set construction of Arveson systems from stationary factorizing measure types. We introduce the notion of a measurable factorizing family of probability measures…
In this paper, we pursue our study of asymptotic properties of families of random matrices that have a tensor structure. In previous work, the first- and second-named authors provided conditions under which tensor products of unitary random…
It is known that a linear hamiltonian system has too many invariant measures, thus the problem of convergence to Gibbs measure has no sense. We consider linear hamiltonian systems of arbitrary finite dimension and prove that, under the…
We present two linear relations between an arbitrary (real tempered second order) generalized stochastic process over $\mathbb{R}^{d}$ and White Noise processes over $\mathbb{R}^{d}$. The first is that any generalized stochastic process can…
We investigate the stabilization of unstable multidimensional partially observed single-sensor and multi-sensor linear systems driven by unbounded noise and controlled over discrete noiseless channels under fixed-rate information…
Denoising diffusions are state-of-the-art generative models exhibiting remarkable empirical performance. They work by diffusing the data distribution into a Gaussian distribution and then learning to reverse this noising process to obtain…
In pattern forming systems such as Rayleigh-Benard convection or directional solidification, a large number of linearly stable, patterned steady states exist when the basic, simple steady state is unstable. Which of these steady states will…
Recent progress in mathematical theory of random processes provides us with non-Fock product systems (continuous tensor products of Hilbert spaces) used here for constructing a toy model for fermions. Some state vectors describe infinitely…
Spectral asymptotics of a tensor product of compact operators in Hilbert space with known marginal asymptotics is studied. Methods of A. Karol', A. Nazarov and Ya. Nikitin (Trans. AMS, 2008) are generalized for operators with almost regular…
We derive the stationary probability distribution for a non-equilibrium system composed by an arbitrary number of degrees of freedom that are subject to Gaussian colored noise and a conservative potential. This is based on a…
Increasingly in recent years, probabilistic computation has been investigated through the lenses of categorical algebra, especially via string diagrammatic calculi. Whereas categories of discrete and Gaussian probabilistic processes have…
We propose a way to construct manifestly gauge independent quantities out of the gauge dependent quantities occurring in the linearized Einstein equations. Thereupon, we show that these gauge-invariant combinations can be identified with…
In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce…
We report the emergence of large-scale hyperuniformity in microfluidic emulsions. Upon periodic driving confined emulsions undergo a first-order transition from a reversible to an irreversible dynamics. We evidence that this dynamical…
In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a nonparametric estimator of the…
Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…
We consider the asymmetric random average process which is a one-dimensional stochastic lattice model with nearest neighbour interaction but continuous and unbounded state variables. First, the explicit functional representations, so-called…