Related papers: New method to study stochastic growth equations: a…
This study focuses on an extended model of a standard cellular automaton (CA) that includes an extra index consisting of a radius that defines a perception area for each cell in addition to the radius defined by the CA rule. Extended…
We introduce the asymmetric extension of the Quantum Symmetric Simple Exclusion Process which is a stochastic model of fermions on a lattice hopping with random amplitudes. In this setting, we analytically show that the time-integrated…
We study the statistical properties of a cellular automata model of traffic flow with the look-ahead potential. The model defines stochastic rules for the movement of cars on a lattice. We analyze the underlying statistical assumptions…
We consider a Markovian growth process on a partially ordered set $\Lambda$, equivalent to last passage percolation (LPP) with independent (not necessarily identical) exponentially distributed weights on the elements of $\Lambda$. Such a…
Motivated by the prediction of cell loads in cellular networks, we formulate the following new, fundamental problem of statistical learning of geometric marks of point processes: An unknown marking function, depending on the geometry of…
Probabilistic cellular automata are prototypes of non equilibrium critical phenomena. This class of models includes among others the directed percolation problem (Domany Kinzel model) and the dynamical Ising model. The critical properties…
Cellular automata (CA) exemplify systems where simple local interaction rules can lead to intricate and complex emergent phenomena at large scales. The various types of dynamical behavior of CA are usually categorized empirically into…
We obtain several exact results for universal distributions involving the maximum of the Airy$_2$ process minus a parabola and plus a Brownian motion, with applications to the 1D Kardar-Parisi-Zhang (KPZ) stochastic growth universality…
We study height fluctuations of interfaces in the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) class, growing at different speeds in the left half and the right half of space. Carrying out simulations of the discrete polynuclear growth…
We review recent progress on the study of the Kardar-Parisi-Zhang (KPZ) equation in a periodic setting, which describes the random growth of an interface in a cylindrical geometry. The main results include central limit theorems for the…
Theory and application of stochastic approximation (SA) have become increasingly relevant due in part to applications in optimization and reinforcement learning. This paper takes a new look at SA with constant step-size $\alpha>0$, defined…
Despite being a key bottleneck in many machine learning tasks, the cost of solving large linear systems has proven challenging to quantify due to problem-dependent quantities such as condition numbers. To tackle this, we consider a…
The growth of stochastic interfaces in the vicinity of a boundary and the non-trivial crossover towards the behaviour deep in the bulk is analysed. The causal interactions of the interface with the boundary lead to a roughness larger near…
For a stochastic system, its evolution from one state to another can have a large number of possible paths. Non-uniformity in the field of system variables leads the local dynamics in state transition varies considerably from path to path…
Random matrix products arise in many science and engineering problems. An efficient evaluation of its growth rate is of great interest to researchers in diverse fields. In the current paper, we reformulate this problem with a generating…
We study the joint probability distribution function (pdf) of the maximum M of the height and its position X_M of a curved growing interface belonging to the universality class described by the Kardar-Parisi-Zhang equation in 1+1…
The Kardar-Parisi-Zhang (KPZ) equation for surface growth has been analyzed for over three decades. Some experiments indicated the power law for the interface width, $w(t)\sim t^\beta$, remains the same as in growth on planar surfaces.…
A generic model of stochastic autocatalytic dynamics with many degrees of freedom $w_i$ $i=1,...,N$ is studied using computer simulations. The time evolution of the $w_i$'s combines a random multiplicative dynamics $w_i(t+1) = \lambda…
We consider a stochastic interface $h(x,t)$, described by the $1+1$ Kardar-Parisi-Zhang (KPZ) equation on the half-line $x\geq0$ with the reflecting boundary at $x=0$. The interface is initially flat, $h(x,t=0)=0$. We focus on the…
We study a stochastic individual-based model of interacting plant and pollinator species through a bipartite graph: each species is a node of the graph, an edge representing interactions between a pair of species. The dynamics of the system…