Related papers: Growth and spectrum of diffusions

Finding the underlying probability distributions of a set of observed sequences under the constraint that each sequence is generated i.i.d by a distinct distribution is considered. The number of distributions, and hence the number of…

We present a simple derivation of an upper bound on the average size of the true vacuum bubbles at the end of inflation, in models of extended inflation type. The derivation uses the inequality that the total energy inside a given volume…

We study a random partial covering model on the $(d-1)$-dimensional unit sphere, where $N$ spherical caps are placed independently and uniformly at random, each covering a surface fraction of $1/N$. This model provides a continuous…

The upper bounds for the rate of fluctuation growth of an observable in both open and closed quantum systems have been studied actively recently. In our recent work we showed that the rate of fluctuation growth for an observable in a closed…

We establish a lower bound for the surface area of a closed, convex hypersurface in Euclidean space in terms of its displacement under continuous maps. As a result, a hypothesized lower bound for the volume of a Riemannian $n$-sphere,…

In many applications, transport of particles can be described by the diffusion equation, or its convective-diffusion generalizations, in part of three-dimensional space. In particular, in surface deposition or in growth of aggregates or…

In this paper we provide a complete proof for a bound on the growth of multi-recurrences which are defined over a number field. The proven bound was already stated by van der Poorten and Schlickewei forty years ago.

The paper provides bounds for the ropelength of a link in terms of the crossing numbers of its split components. As in earlier papers, the bounds grow with the square of the crossing number; however, the constant involved is a substantial…

Consider a uniform expanders family G_n with a uniform bound on the degrees. It is shown that for any p and c>0, a random subgraph of G_n obtained by retaining each edge, randomly and independently, with probability p, will have at most one…

The analysis of the size distribution of droplets condensing on a substrate (breath figures) is a test ground for scaling theories. Here, we show that a faithful description of these distributions must explicitly deal with the growth…

We extend below a limit theorem of Baker, Chigansky, Hamza and Klebaner (2018) for diffusion models used in population theory.

We study the connections between volume growth, spectral properties and stochastic completeness of locally finite graphs. For a class of graphs with a very weak spherical symmetry we give a condition which implies both stochastic…

For critical bond-percolation on high-dimensional torus, this paper proves sharp lower bounds on the size of the largest cluster, removing a logarithmic correction in the lower bound in Heydenreich and van der Hofstad (2007). This…

We use spectral embeddings to give upper bounds on the spectral function of the Laplace--Beltrami operator on homogeneous spaces in terms of the volume growth of balls. In the case of compact manifolds, our bounds extend the 1980 lower…

We draw a figure from where it is possible to measure the number of e-folds of expansion of the universe with a ruler. We find model independent bounds for the number of e-folds during inflation, reheating and radiation. We also give a…

Let $X$ be an algebraic variety, defined over the rationals. This paper gives upper bounds for the number of rational points on $X$, with height at most $B$, for the case in which $X$ is a curve or a surface. In the latter case one excludes…

We give a lower bound for the degree of a finite cover of a hyperbolic 3-manifold which fibers over the circle, in terms of volume, the diameter of the manifold and other new invariants.

We improve the known upper bound for short exponential sums and increase the range on which a sharp upper bound is known.

Hydrodynamic projections, the projection onto conserved charges representing ballistic propagation of fluid waves, give exact transport results in many-body systems, such as the exact Drude weights. Focussing one one-dimensional systems, I…

We elaborate on the intimate connection between the largest volume of an empty axis-parallel box in a set of $n$ points from $[0,1]^d$ and cover-free families from the extremal set theory. This connection was discovered in a recent paper of…