Related papers: Stationary measures for the Porous Medium Model
The filtration of fluid in 2D porous medium is simulated by the molecular dynamics technique. The high concentration of fluid is created at the initial point in time and the number of fluid particles is investigated in all porous. The…
We consider a hypothesis testing problem for displacement parameters of n independent copies of an m-mode squeezed quantum Gaussian state whose mixture parameter is known. Given n>1, we construct a quantum measurement as a test using an…
This paper focuses on estimating the invariant density function $f_X$ of the strongly mixing stationary process $X_t$ in the multiplicative measurement errors model $Y_t = X_t U_t$, where $U_t$ is also a strongly mixing stationary process.…
The dynamics of a system, made of a particle interacting with a field mode, thwarted by the action of repeated projective measurements on the particle, is examined. The effect of the partial measurements is discussed by comparing it with…
We are interested in studying the stationary solutions and phase transitions of aggregation equations with degenerate diffusion of porous medium-type, with exponent $1 < m < \infty$. We first prove the existence of possibly infinitely many…
This article studies the quasi-stationary behaviour of multidimensional birth and death processes, modeling the interaction between several species, absorbed when one of the coordinates hits 0. We study models where the absorption rate is…
We study measure-theoretical aspects of torus piecewise isometries. Not much is known about this type of dynamical systems, except for the special case of one-dimensional interval exchange mappings. The last case is fundamentally different…
A simple variogram model with two parameters is presented that includes the power variogram for the fractional Brownian motion, a modified De Wijsian model, the generalized Cauchy model and the multiquadrics model. One parameter controls…
Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations (PDEs) are a popular tool for modelling such phenomena deterministically, but it is often necessary to use…
We consider totally asymmetric simple exclusion processes with n types of particle and holes ($n$-TASEPs) on $\mathbb {Z}$ and on the cycle $\mathbb {Z}_N$. Angel recently gave an elegant construction of the stationary measures for the…
Mutual unbiasedness of the eigenstates of phase-space operators-such as position and momentum, or their standard coarse grained versions-exists only in the limiting case of infinite squeezing. In [Phys. Rev. Lett. 120, 040403 (2018)] it was…
We introduce the Mass Migration Process (MMP), a conservative particle system on ${\mathbb N}^{{\mathbb Z}^d}$. It consists in jumps of $k$ particles ($k\ge 1$) between sites, with a jump rate depending only on the state of the system at…
We introduce a symmetric, gradient exclusion process within the class of non-cooperative kinetically constrained lattice gases, modelling a non-linear diffusivity in which the exchange of occupation values between two neighbouring sites…
The jamming transition is an important feature of granular materials, with prior work showing an excess of low frequency modes in the granular analog to the density of states, the granular density of modes. In this work, we present an…
Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy…
Exchangeability -- in which the distribution of an infinite sequence is invariant to reorderings of its elements -- implies the existence of a simple conditional independence structure that may be leveraged in the design of statistical…
This paper provides unified calculations regarding certain measures and transformations in interacting particle systems. More specifically, we provide certain general conditions under which an interacting particle system will have a…
A change of variables is introduced to reduce certain nonlinear stochastic evolution equations with multiplicative noise to the corresponding deterministic equation. The result is then used to investigate a stochastic porous medium…
Measurement models (MMs) stand at the highest structural level of quantum measurement theory. MMs can be employed to construct instruments which stand at the next level. An instrument is thought of as an apparatus that is used to measure…
In several application fields like daily pluviometry data modelling, or motion analysis from image sequences, observations contain two components of different nature. A first part is made with discrete values accounting for some symbolic…