Related papers: Non-fixation for conservative stochastic dynamics …
We study a model of random walk on a fluctuating rough surface using the field-theoretic renormalization group (RG). The surface is modelled by the well-known Kardar--Parisi--Zhang (KPZ) stochastic equation while the random walk is…
We define the Uniform Random Walk (URW) on a connected, locally finite graph as the weak limit of the uniform walk of length $n$ starting at a fixed vertex. When the limit exists, it is necessarily Markovian and is independent of the…
Intermittent stochastic processes appear in a wide field, such as chemistry, biology, ecology, and computer science. This paper builds up the theory of intermittent continuous time random walk (CTRW) and L\'{e}vy walk, in which the…
Standard continuous time random walk (CTRW) models are renewal processes in the sense that at each jump a new, independent pair of jump length and waiting time are chosen. Globally, anomalous diffusion emerges through action of the…
Random walk models, such as the trap model, continuous time random walks, and comb models exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is: what statistical mechanical theory replaces the…
The dynamics of interacting domain walls, regarded as a system of particles which are biased to move towards their nearest neighbours and annihilate when they meet, have been studied in the recent past. We study the effect of the presence…
We study a system of $N$ interacting particles on $\bf{Z}$. The stochastic dynamics consists of two components: a free motion of each particle (independent random walks) and a pair-wise interaction between particles. The interaction belongs…
The parity conserving branching-annihilating random walk (pc-BARW) model is a reaction-diffusion system on a lattice where particles can branch into $m$ offsprings with even $m$ and hop to neighboring sites. If two or more particles land on…
We introduce a new random walk with unbounded memory obtained as a mixture of the Elephant Random Walk and the Dynamic Random Walk which we call the Dynamic Elephant Random Walk (DERW). As a consequence of this mixture the distribution of…
Recent research in both the experimental and mathematical communities has focused on biochemical interaction systems that satisfy an "absolute concentration robustness" (ACR) property. The ACR property was first discovered experimentally…
We consider one-dimensional excited random walks (ERWs) with i.i.d. markovian cookie stacks in the non-boundary recurrent regime. We prove that under diffusive scaling such an ERW converges in the standard Skorokhod topology to a multiple…
Jamming is a phenomenon shared by a wide variety of systems, such as granular materials, foams, and glasses in their high density regime. This has motivated the development of a theoretical framework capable of explaining many of their…
We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on…
We consider continuous time random walks (CTRW) for open systems that exchange energy and matter with multiple reservoirs. Each waiting time distribution (WTD) for times between steps is characterized by a positive parameter a, which is set…
We present our recent work on stochastic particle systems on complex networks. As a noninteracting system we first consider the diffusive motion of a random walker on heterogeneous complex networks. We find that the random walker is…
We present an exact solution for one-dimensional overdamped dynamics near a hard wall, allowing us to connect steady-state distributions under confinement with the extreme value statistics of unconfined stochastic processes. This mapping…
We study a recently introduced ladder model which undergoes a transition between an active and an infinitely degenerate absorbing phase. In some cases the critical behaviour of the model is the same as that of the branching annihilating…
We consider the simple random walk on the infinite cluster of a general class of percolation models on $\mathbb{Z}^d$, $d\geq 3$, including Bernoulli percolation as well as models with strong, algebraically decaying correlations. For almost…
It has recently been shown that structural conditions on the reaction network, rather than a 'fine-tuning' of system parameters, often suffice to impart 'absolute concentration robustness' on a wide class of biologically relevant,…
It is known that simulation of the mean position of a Reflected Random Walk (RRW) $\{W_n\}$ exhibits non-standard behavior, even for light-tailed increment distributions with negative drift. The Large Deviation Principle (LDP) holds for…