Related papers: Can a Lamb Reach a Haven Before Being Eaten by Dif…
The survival probability, S_N(t), of a diffusing prey (``lamb'') in the proximity of N diffusing predators (a ``pride of lions'') in one dimension is investigated. When the lions are all to one side of the lamb, the survival probability…
We study the capture of a diffusing "lamb" by diffusing "lions" in one dimension. The capture dynamics is exactly soluble by probabilistic techniques when the number of lions is very small, and is tractable by extreme statistics…
We study the escape behavior of a lamb to safe haven pursued by a hungry lion. Identifying the system with a pair of vicious Brownian walkers we evaluate the probability density function for the vicious pair and from there we estimate the…
We study the dynamical properties of a diffusing lamb captured by a diffusing lion on the complex networks with various sizes of $N$. We find that the life time <T>$ of a lamb scales as <T>\sim N$ and the survival probability $S(N\to…
A diffusing lion pursues a diffusing lamb when both of them are allowed to get back to their homes intermittently. Identifying the system with a pair of vicious random walkers, we study their dynamics under Poissonian and sharp resetting.…
We study the survival of a prey that is hunted by N predators. The predators perform independent random walks on a square lattice with V sites and start a direct chase whenever the prey appears within their sighting range. The prey is…
The predator/prey (capture) problem is a prototype of many network-related applications. We study the capture process on complex networks by considering multiple predators from multiple sources. In our model, some lions start from multiple…
We study the splitting probabilities for a one-dimensional Brownian motion in a cage whose two boundaries move at constant speeds $c_1$ and $c_2$. This configuration corresponds to the capture of a diffusing, but skittish lamb, with an…
We consider non-interacting particles (or lions) performing one-dimensional random walks or L\'evy flights (with L\'evy index $1 < \mu \leq 2$) in the presence of a constant drift $c$. Initially these random walkers are uniformly…
Be $X_t$ a random walk. We study its span $S$, i.e. the size of the domain visited up to time $t$. We want to know the probability that $S$ reaches $1$ for the first time, as well as the density of the span given $t$. Analytical results are…
We calculate the exact asymptotic survival probability, Q, of a one-dimensional Brownian particle, initially located located at the point x in (-L,L), in the presence of two moving absorbing boundaries located at \pm(L+ct). The result is…
The problem of a diffusing particle moving among diffusing traps is analyzed in general space dimension d. We consider the case where the traps are initially randomly distributed in space, with uniform density rho, and derive upper and…
We consider one-dimensional discrete-time random walks (RWs) in the presence of finite size traps of length $\ell$ over which the RWs can jump. We study the survival probability of such RWs when the traps are periodically distributed and…
We study the survival probability of an immobile target in presence of N independent diffusing walkers. We address the problem of the Mean Target Lifetime and its dependence on the number and initial distribution of the walkers when the…
We investigate condensation phase transitions of symmetric conserved-mass aggregation (SCA) model on random networks (RNs) and scale-free networks (SFNs) with degree distribution $P(k) \sim k^{-\gamma}$. In SCA model, masses diffuse with…
We analyze a trapping reaction with a single penetrable trap, in a one dimensional lattice, where both species (particles and trap) are mobile and have a drift velocity. We obtain the density as seen from a reference system attached to the…
The asymptotic survival probability of a spherical target in the presence of a single subdiffusive trap or surrounded by a sea of subdiffusive traps in a continuous Euclidean medium is calculated. In one and two dimensions the survival…
We consider a one-dimensional Brownian motion with diffusion coefficient $D$ in the presence of $n$ partially absorbing traps with intensity $\beta$, separated by a distance $L$ and evenly spaced around the initial position of the particle.…
Nearest neighbor random walks in the quarter plane that are absorbed when reaching the boundary are studied. The cases of positive and zero drift are considered. Absorption probabilities at a given time and at a given site are made…
Reaction-diffusion process with exclusion in the presence of traps has been studied. The asymptotic survival probability for the case of uniformly distributed random traps shows a stretched e\ xponential behavior. We show that additional…