Related papers: Rescaling the spatial lambda Fleming-Viot process …
We search for time-dependent solutions for the 5-dimensional system of a scalar field canonically coupled to gravity. Time-independent and time-dependent scalar field configurations with the most general homogeneous and isotropic 4D metric…
The recent transition from decelerated to accelerated expansion can be seen as a reflection (or "bounce") in the connection variable, defined by the inverse comoving Hubble length ($b=\dot a$, on-shell). We study the quantum cosmology of…
A new energy-based stochastic extension of the Schrodinger equation for which the wave function collapses after the passage of a finite amount of time is proposed. An exact closed-form solution to the dynamical equation, valid for all…
The treatment of a quantized field in a curved spacetime requires the study of backreaction of the field on the spacetime via the semiclassical Einstein equation. We consider a free scalar field in spatially flat Robertson-Walker space…
We introduce a transform on the class of stochastic exponentials for d-dimensional Brownian motions. Each stochastic exponential generates another stochastic exponential under the transform. The new exponential process is often merely a…
Using two different methods, we have determined the rescaling of the scalar condensate $Z\equiv Z_\phi$ near the critical line of a 4D Ising model. Our lattice data, in agreement with previous numerical indications, support the behavior…
We develop a semiclassical approximation scheme for the constraint equations of supersymmetric canonical quantum gravity. This is achieved by a Born-Oppenheimer type of expansion, in analogy to the case of the usual Wheeler-DeWitt equation.…
We study the scaling limits of genealogical trees arising from Cannings models. Under suitable moment conditions, we show that the rescaled contour and height functions converge to a time change of Brownian motion conditioned on a given…
In this work the role of extra dimensions in the accelerated universe through the scenario of higher-dimensional Friedmann-Robertson-Walker (FRW) cosmology has been studied. For this purpose, we first consider warped space-time in the…
We build upon previous investigation of the one-dimensional conformal symmetry of the Friedman-Lema\^ itre-Robertson-Walker (FLRW) cosmology of a free scalar field and make it explicit through a reformulation of the theory at the classical…
We consider a model of Branching Brownian Motion in which the usual spatially-homogeneous and catalytic branching at a single point are simultaneously present. We establish the almost sure growth rates of population in certain…
We consider Brownian motions with one-sided collisions, meaning that each particle is reflected at its right neighbour. For a finite number of particles a Sch\"{u}tz-type formula is derived for the transition probability. We investigate an…
We present a new proof of the extended arc-sine law related to Walsh's Brownian motion, known also as Brownian spider. The main argument mimics the scaling property used previously, in particular by D. Williams in the 1-dimensional Brownian…
We extend the spatial $\Lambda$-Fleming-Viot process introduced in [Electron. J. Probab. 15 (2010) 162-216] to incorporate recombination. The process models allele frequencies in a population which is distributed over the two-dimensional…
We obtain a time-dependent Schrodinger equation for the Friedmann - Robertson - Walker (FRW) model interacting with a homogeneous scalar matter field. We show that for this purpose it is necesary to include an additional action invariant…
We extend existing connections between random walks, branching processes, and spatial branching processes, and their respective scaling limits, to include processes in dependent random environments. More specifically, we prove new scaling…
We show that the range of a long Brownian bridge in the hyperbolic space converges after suitable renormalisation to the Brownian continuum random tree. This result is a relatively elementary consequence of $\bullet$ A theorem by Bougerol…
The dynamical effect of the cosmological constant $\Lambda$ on a single spherical void evolving in a the universe is investigated within a non linear perturbation of Newton-Friedmann models. The void expands with a huge initial burst which…
We consider time-periodic patterns of the dissipative three dimensional baroclinic quasigeostrophic model in spherical coordinates, under time-dependent forcing. We show that when the forcing is time-periodic and the spatial square-integral…
We define and study in detail \emph{utraslow scaled Brownian motion (USBM)\/} characterised by a time dependent diffusion coefficient of the form $D(t)\simeq 1/t$. For unconfined motion the mean squared displacement (MSD) of USBM exhibits…