Related papers: Rescaling the spatial lambda Fleming-Viot process …

The Lamperti transform offers a powerful bridge between self-similar processes and stationary dynamics, making it especially useful for analyzing anomalous diffusion models that lack stationary increments. In this paper we examine the…

In the large extra dimensional braneworld inflation, Friedmann equation is modified to include a quadratic term in energy density with an additional parameter $\lambda$ called brane tension in addition to the usual linear term. The high…

We investigate the dynamics of the Friedmann-Lema\^itre-Robertson-Walker spacetime within the framework of $f(R)$ gravity using a compact, model-independent dynamical systems approach. By assuming a power-law scale factor, we explore…

We implement a conformal time scale factor duality for Friedmann-Robertson-Walker cosmological models, which is consistent with the weak energy condition. The requirement for self-duality determines the equations of state for a broad class…

This article introduces a novel construction of the two-dimensional fractional Brownian motion (2D fBm) with dependent components. Unlike similar models discussed in the literature, our approach uniquely accommodates the full range of model…

Consider a time-varying collection of n points on the positive real axis, modeled as exponentials of n Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. If…

We show that the accelerated expansion of the Universe can be viewed as a crossover phenomenon where the Newton constant and the Cosmological constant are actually scaling operators, dynamically evolving in the attraction basin of a…

In this paper, we analyze the asymptotic behavior of the point process of exceedances in a spatio-temporal setting whose points are given by the rescaled occurrence times, the sites and the rescaled values of exceedances. Here, the…

Consider a random walker on the nonnegative lattice, moving in continuous time, whose positive transition intensity is proportional to the time the walker spends at the origin. In this way, the walker is a jump process with a stochastic and…

This paper is a follow-up of the work initiated in [3], where it has been investigated the hydrodynamic limit of symmetric independent random walkers with birth at the origin and death at the rightmost occupied site. Here we obtain two…

We investigate refocusing and strong refocusing of light rays in a space-time. A strongly refocusing space-time is refocusing. The converse is unknown. We construct examples of space-times which are refocusing, but not strongly so, at a…

We prove that, after suitable rescaling, the simple random walk on the trace of a large critical branching random walk converges to the Brownian motion on the integrated super-Brownian excursion.

Consider a continuous time Markov chain with rates Q in the state space \Lambda\cup\{0\} with 0 as an absorbing state. In the associated Fleming-Viot process N particles evolve independently in \Lambda with rates Q until one of them…

Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed…

We consider the large deviations of the hydrodynamic rescaling of the zero-range process on $\mathbb{Z}^d$ in any dimension $d\ge 1$. Under mild and canonical hypotheses on the local jump rate, we obtain matching upper and lower bounds,…

We consider a 2-dimensional model of random walk in random environment known as line model. The environment is described by two independent families of i.i.d. random variables dictating rates of jumps in vertical, respectively horizontal…

This paper provides a multivariate extension of Bertoin's pathwise construction of a L\'evy process conditioned to stay positive/negative. Thus obtained processes conditioned to stay in half-spaces are closely related to the original…

We prove that adiabatic regularization and DeWitt-Schwinger point-splitting provide the same result for the renormalized expectation values of the stress-energy tensor for spin-$1/2$ fields. This generalizes the equivalence found for scalar…

Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…

We present a new class of oscillons in the (1+1)-dimensional signum-Gordon model. The oscillons periodically move to and fro in the space. They have finite total energy, finite size, and are strictly periodic in time. The corresponding…