Related papers: Frog model on $\mathbb{Z}$ with random survival pa…
We consider the Activated Random Walk model on $\mathbb{Z}$. In this model, each particle performs a continuous-time simple symmetric random walk, and falls asleep at rate $\lambda$. A sleeping particle does not move but it is reactivated…
We study a one-dimensional lattice random walk with an absorbing boundary at the origin and a movable partial reflector. On encountering the reflector, at site x, the walker is reflected (with probability r) to x-1 and the reflector is…
A survival model is derived from the exponential function using the concept of fractional differentiation. The hazard function of the proposed model generates various shapes of curves including increasing, increasing-constant-increasing,…
A dynamic model for a random network evolving in continuous time is defined where new vertices are born and existing vertices may die. The fitness of a vertex is defined as the accumulated in-degree of the vertex and a new vertex is…
The object of study is a soft random geometric graph with vertices given by a Poisson point process on a line and edges between vertices present with probability that has a polynomial decay in the distance between them. Various aspects of…
We consider a one-dimensional simple random walk surviving among a field of static soft traps : each time it meets a trap the walk is killed with probability 1--e --$\beta$ , where $\beta$ is a positive and fixed parameter. The positions of…
A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of…
The frog model is an infection process in which dormant particles begin moving and infecting others once they become infected. We show that on the rooted $d$-ary tree with particle density $\Omega(d^2)$, the set of visited sites contains a…
We consider a mortal random walker on a family of hierarchical graphs in the presence of some trap sites. The configuration comprising the graph, the starting point of the walk, and the locations of the trap sites is taken to be exactly…
Place an active particle at the root of the infinite $d$-ary tree and dormant particles at each non-root site. Active particles move towards the root with probability $p$ and otherwise move to a uniformly sampled child vertex. When an…
We consider the branching random walk in random environment with a random absorption wall. When we add this barrier, we discuss some topics related to the survival probability. We assume that the random environment is i.i.d., $S_i$ is a…
We consider the static and dynamic phases in a Rosenzweig-Porter (RP) random matrix ensemble with the tailed distribution of off-diagonal matrix elements of the form of the large-deviation ansatz. We present a general theory of survival…
We consider a random walk with death in $[-N,N]$ moving in a time dependent environment. The environment is a system of particles which describes a current flux from $N$ to $-N$. Its evolution is influenced by the presence of the random…
The frog model is a growing system of random walks where a particle is added whenever a new site is visited. A longstanding open question is how often the root is visited on the infinite $d$-ary tree. We prove the model undergoes a phase…
We consider a parametric modelling approach for survival data where covariates are allowed to enter the model through multiple distributional parameters, i.e., scale and shape. This is in contrast with the standard convention of having a…
We provide sufficient conditions for the validity of a dichotomy, i.e. zero-one law, between recurrence and transience of general frog models. In particular, the results cover frog models with i.i.d. numbers of frogs per site where the frog…
Multiple species in the ecosystem are believed to compete cyclically for survival and thus maintain balance in nature. Stochasticity has also an inevitable role in this dynamics. Considering these attributes of nature, the stochastic…
We study the recurrence of one-per-site frog model $\text{FM}(d, p)$ on a $d$-ary tree with drift parameter $p\in [0,1]$, which determines the bias of frogs' random walks. We are interested in the minimal drift $p_{d}$ so that the frog…
We study the branching random walk on weighted graphs; site-breeding and edge-breeding branching random walks on graphs are seen as particular cases. We describe the strong critical value in terms of a geometrical parameter of the graph. We…
We present a detailed comparison of the motion of a classical and of a quantum particle in the presence of trapping sites, within the framework of continuous-time classical and quantum random walk. The main emphasis is on the qualitative…