Related papers: The $\Lambda$-coalescent speed of coming down from…
A covariant way to define the relativistic entropy of a finite object has been proposed. The energy-momentum of an object with finite volume is not a covariant physical entity because of the relativity of simultaneity. A way to correctly…
An infinite sequence of 0's and 1's evolves by flipping each~1 to a~0 exponentially at rate one. When a~1 flips, all bits to its right also flip. Starting from any configuration with finitely many 1's to the left of the origin, we show that…
We explore freezing dark energy, where the evolution of the field approaches that of a cosmological constant at late times. We propose two general, two parameter forms to describe the class of freezing field models, in analogy to ones for…
Some physical aspects related to the limit operations of the Thomson lamp are discussed. Regardless of the formally unbounded and even infinite number of "steps" involved, the physical limit has an operational meaning in agreement with the…
In an optimal control framework, we consider the value $V_T(x)$ of the problem starting from state $x$ with finite horizon $T$, as well as the value $V_\lambda(x)$ of the $\lambda$-discounted problem starting from $x$. We prove that uniform…
The main result of the article reads: the distribution of a continuous starting from zero local martingale whose quadratic characteristic is almost surely absolutely continuous with respect to some non-random increasing continuous function…
We study the height of the maximal particle at time $t$ of a one dimensional branching Brownian motion with a space-dependent branching rate. The branching rate is set to zero in finitely many intervals (obstacles) of order $t$. We obtain…
We prove several limit theorems that relate coalescent processes to continuous-state branching processes. Some of these theorems are stated in terms of the so-called generalized Fleming-Viot processes, which describe the evolution of a…
A time-varying cosmological "constant" Lambda is consistent with Einstein's equation, provided matter and/or radiation is created or destroyed to compensate for it. Supposing an empty primordial universe endowed with a very large…
We consider the possibility that the dark sector of our Universe contains a negative cosmological constant dubbed $\lambda$. For such models to be viable, the dark sector should contain an additional component responsible for the late-time…
In the $\Lambda$CDM model, dark energy is viewed as a constant vacuum energy density, the cosmological constant in the Einstein--Hilbert action. This assumption can be relaxed in various models that introduce a dynamical dark energy. In…
Dynamical wave function collapse models entail the continuous liberation of a specified rate of energy arising from the interaction of a fluctuating scalar field with the matter wave function. We consider the wave function collapse process…
The paper presents the transition of universe from early decelerating phase to current accelerating phase with viscous fluid and time dependent cosmological constant $(\Lambda)$ as source of matter in Bianchi-V space-time. To study the…
We consider a system of annihilating particles where particles start from the points of a Poisson process on the line, move at constant i.i.d. speeds symmetrically distributed in {-1,0,+1} and annihilate upon collision. We prove that…
Given a nondecreasing sequence $\Lambda=\{\lambda_n>0\}$ such that $\displaystyle\lim_{n\to\infty} \lambda_n=\infty,$ we consider the sequence $\mathcal N_\Lambda:=\left\{\lambda_ne^{i\theta_n},n\in\,\mathbb N\right\}$, where $\theta_n$ are…
On the real line initially there are infinite number of particles on the positive half-line., each having one of $K$ negative velocities $v_{1}^{(+)},...,v_{K}^{(+)}$. Similarly, there are infinite number of antiparticles on the negative…
We show that the total number of collisions in the exchangeable coalescent process driven by the beta $(1,b)$ measure converges in distribution to a 1-stable law, as the initial number of particles goes to infinity. The stable limit law is…
In 1997, an extension of general relativity was proposed that predicts the dark energy density \Lambda\ to vary linearly with the total number of macroscopic black holes in the universe. We explore this prediction and find that \Lambda\…
We provide a rigorous derivation of the brownian motion as the limit of a deterministic system of hard-spheres as the number of particles $N$ goes to infinity and their diameter $\varepsilon$ simultaneously goes to $0$, in the fast…
We consider a branching Brownian motion in which binary fission takes place only when particles are at the origin at a rate \beta > 0 on the local time scale. We obtain results regarding the asymptotic behaviour of the number of particles…