Related papers: The Frog Model on $\mathbb{Z}$ with Discrete Weibu…
Assume that $N_m(x)$ denotes the density of the population at a point $x$ at the beginning of the reproductive season in the $m$th year. We study the following impulsive reaction-diffusion model for any $m\in \mathbb Z^+$…
Predicting evolution of expanding populations is critical to control biological threats such as invasive species and cancer metastasis. Expansion is primarily driven by reproduction and dispersal, but nature abounds with examples 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…
In this paper we study two natural models of \textit{random temporal} graphs. In the first, the \textit{continuous} model, each edge $e$ is assigned $l_e$ labels, each drawn uniformly at random from $(0,1]$, where the numbers $l_e$ are…
We consider the system of $N$ one-dimensional free fermions confined by a harmonic well $V(x) = m\omega^2 {x^2}/{2}$ at finite inverse temperature $\beta = 1/T$. The average density of fermions $\rho_N(x,T)$ at position $x$ is derived. For…
The frog model starts with one active particle at the root of a graph and some number of dormant particles at all nonroot vertices. Active particles follow independent random paths, waking all inactive particles they encounter. We prove…
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…
The long time behaviour of the survival probability of initial state and its dependence on the initial states are considered, for the one dimensional free quantum particle. We derive the asymptotic expansion of the time evolution operator…
Time evolution of number of species (genera, families, and others), population of them, and size distribution of present ones and life times are studied in terms of a new model, where population of each genetic taxon increases by a (random)…
Reliability inference based on parametric distributions is an important problem in electrical and mechanical engineering. Most existing methods rely on approximations or bootstrap procedures, which may not perform satisfactorily when data…
Most theoretical analysis for lifetime distribution explains origins of specific distribution based on independent failure. We develop a unified framework encompassing different lifetime distribution for failure-coupled network systems. We…
We investigate the survival probability of a localized 1-d quantum particle subjected to a time dependent potential of the form $rU(x)\sin{\omega t}$ with $U(x)=2\delta (x-a)$ or $U(x)= 2\delta(x-a)-2\delta (x+a)$. The particle is initially…
We study a system of random walks, known as the frog model, starting from a profile of independent Poisson($\lambda$) particles per site, with one additional active particle planted at some vertex $\mathbf{o}$ of a finite connected simple…
We study the dynamic response of a two-dimensional system of itinerant fermions in the vicinity of a uniform ($\mathbf{Q}=0$) Ising nematic quantum critical point of $d-$wave symmetry. The nematic order parameter is not a conserved…
We study the discrete-time dynamical systems of a model of wild mosquito population with distinct birth (denoted by $\beta$) and death (denoted by $\mu$) rates. The case $\mu=\beta$ was considered in our previous work. In this paper we…
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…
We establish both extinction and non-extinction self-similar profiles for the following fast diffusion equation with a weighted source term $$ \partial_tu=\Delta u^m+|x|^{\sigma}u^p, $$ posed for $(x,t)\in\real^N\times(0,\infty)$, $N\geq3$,…
We study the late time exponential decay of the survival probability $S_\pm(t,a|x_0)\sim e^{-\theta(a)t}$, of a one-dimensional run and tumble particle starting from $x_0<a$ with an initial orientation $\sigma(0)=\pm 1$, under a confining…
We consider the extreme value theory of a hyperbolic toral automorphism $T: \mathbb{T}^2 \to \mathbb{T}^2$ showing that if a H\"older observation $\phi$ which is a function of a Euclidean-type distance to a non-periodic point $\zeta$ is…
Extinction times in resampling processes are fundamental yet often intractable, as previous formulas scale as $2^M$ with the number of states $M$ present in the initial probability distribution. We solve this by treating multinomial updates…