Related papers: Zero-range process in random environment
We study the motion of independent particles in a dynamical random environment on the integer lattice. The environment has a product distribution. For the multidimensional case, we characterize the class of spatially ergodic invariant…
We consider a random walk in $\mathbb Z^d$ which jumps from a site $x$ to a nearest neighboring site $x+e$ (where $e\in V:=\{x\in\mathbb Z^d: |x|_1=1\}$) with probability $p_0(e)+\epsilon\xi(x,e)$. Here $\sum_e p_0(e)=1$, $p_0(e)> 0$,…
A simple optimization scheme is used to compute the density-density response function of an electron liquid. Higher order terms in the perturbation expansion beyond the random phase approximation are summed approximately by enforcing the…
Hydrodynamic systems arising in swarming modelling include nonlocal forces in the form of attractive-repulsive potentials as well as pressure terms modelling strong local repulsion. We focus on the case where there is a balance between…
We study random walks on $\mathbb{Z}$ which have a linear (or almost linear) drift towards 0 in a range around 0. This drift leads to a metastable Gaussian distribution centered at zero. We give specific, fast growing, time windows where we…
We study a zero-range process where the jump rates do not only depend on the local particle configuration, but also on the size of the system. Rigorous results on the equivalence of ensembles are presented, characterizing the occurrence of…
Random walks in random scenery are processes defined by $Z_n:=\sum_{k=1}^n\xi_{X_1+...+X_k}$, where $(X_k,k\ge 1)$ and $(\xi_y,y\in\mathbb Z)$ are two independent sequences of i.i.d. random variables. We assume here that their distributions…
L\'evy walk process is one of the most effective models to describe superdiffusion, which underlies some important movement patterns and has been widely observed in the micro and macro dynamics. From the perspective of random walk theory,…
A random walk in a sparse random environment is a model introduced by Matzavinos et al. [Electron. J. Probab. 21, paper no. 72: 2016] as a generalization of both a simple symmetric random walk and a classical random walk in a random…
We introduce random walks in a sparse random environment on $\mathbb Z$ and investigate basic asymptotic properties of this model, such as recurrence-transience, asymptotic speed, and limit theorems in both the transient and recurrent…
For a homogeneous random walk in the quarter plane with nearest-neighbor transitions, starting from some state $(i_0,j_0)$, we study the event that the walk reaches the vertical axis, before reaching the horizontal axis. We derive an exact…
Optimizing the energy efficiency of driving processes provides valuable insights into the underlying physics and is of crucial importance for numerous applications, from biological processes to the design of machines and robots. Knowledge…
We calculate the exact stationary distribution of the one-dimensional zero-range process with open boundaries for arbitrary bulk and boundary hopping rates. When such a distribution exists, the steady state has no correlations between sites…
We find that, in the presence of weak incoherent effects from surrounding environments, the zero temperature conductance of nearest neighbour tight-binding chains exhibits a counter-intuitive power-law growth with system length at…
We consider the one-dimensional asymmetric zero-range process starting from a step decreasing profile. In the hydrodynamic limit this initial condition leads to the rarefaction fan of the associated hydrodynamic equation. Under this initial…
The integer points (sites) of the real line are marked by the positions of a standard random walk. We say that the set of marked sites is weakly, moderately or strongly sparse depending on whether the jumps of the standard random walk are…
We study the random walk in random environment on {0,1,2,...}, where the environment is subject to a vanishing (random) perturbation. The two particular cases we consider are: (i) random walk in random environment perturbed from Sinai's…
We consider the optimal scaling problem for high-dimensional random walk Metropolis (RWM) algorithms where the target distribution has a discontinuous probability density function. Almost all previous analysis has focused upon continuous…
Random walks provide a simple conventional model to describe various transport processes, for example propagation of heat or diffusion of matter through a medium. However, in many practical cases the medium is highly irregular due to…
A central goal of thermodynamics is to identify optimal processes during which the least amount of energy is dissipated into the environment. Generally, even for simple systems, such as the parametric harmonic oscillator, optimal control…