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Let $K_n$ be the convex hull of i.i.d. random variables distributed according to the standard normal distribution on $\R^d$. We establish variance asymptotics as $n \to \infty$ for the re-scaled intrinsic volumes and $k$-face functionals of…
We establish necessary and sufficient conditions implying that the product of $m\geq 2$ Poisson functionals, living in a finite sum of Wiener chaoses, is square-integrable. Our conditions are expressed in terms of iterated add-one cost…
Learning, especially rapid learning, is critical for survival. However, learning is hard: a large number of synaptic weights must be set based on noisy, often ambiguous, sensory information. In such a high-noise regime, keeping track of…
For Gaussian random fields with values in $\mathbb{R}^d$, sharp upper and lower bounds on the probability of hitting a fixed set have been available for many years. These apply in particular to the solutions of systems of linear SPDEs. For…
We study a spatial branching model, where the underlying motion is $d$-dimensional ($d\ge1$) Brownian motion and the branching rate is affected by a random collection of reproduction suppressing sets dubbed mild obstacles. The main result…
We show that the random point measures induced by vertices in the convex hull of a Poisson sample on the unit ball, when properly scaled and centered, converge to those of a mean zero Gaussian field. We establish limiting variance and…
We describe methods for proving upper and lower bounds on infinite-time averages in deterministic dynamical systems and on stationary expectations in stochastic systems. The dynamics and the quantities to be bounded are assumed to be…
Considering the dynamics of a polymer with finite extensibility placed in a chaotic flow with large mean shear, we explain how the statistics of polymer extension changes with Weissenberg number, ${\it Wi}$, defined as the product of the…
We consider a one-dimensional Brownian motion with diffusion coefficient $D$ in the presence of $n$ partially absorbing traps with intensity $\beta$, separated by a distance $L$ and evenly spaced around the initial position of the particle.…
We study the statistical and dynamic properties of the systems characterized by an ultrametric space of states and translationary non-invariant symmetric transition matrices of the Parisi type subjected to "locally constant" randomization.…
Motivated by the study of the directed polymer model with mobile Poissonian traps or catalysts and the stochastic parabolic Anderson model with time dependent potential, we investigate the asymptotic behavior of…
We investigate the global existence of weak solutions to a free boundary problem governing the evolution of finitely extensible bead-spring chains in dilute polymers. The free boundary in the present context is defined with regard to a…
Bayesian, classical, and extended maximum likelihood approaches to estimation of upper limits in experiments with small numbers of signal events are surveyed. The discussion covers only experiments whose outcomes are well described by a…
We consider two models of random diffusion in random environment in two dimensions. The first example is the self-repelling Brownian polymer, this describes a diffusion pushed by the negative gradient of its own occupation time measure…
Working in pressureless magnetohydrodynamics, we examine the consequences of some peculiar dispersive properties of linear fast sausage modes (FSMs) in one-dimensional cylindrical equilibria with a continuous radial density profile…
We employ computer simulations to study the dynamics of a self-propelled spherical tracer particle in a viscoelastic medium, made of a long polymer chain. Here, the interplay between viscoelasticity, stickiness, and activity…
We study the conformations of polymer chains in a poor solvent, with and without bending rigidity, by means of a simple statistical mechanics model. This model can be exactly solved for chains of length up to N=55 using exact enumeration…
We consider the classical two-dimensional Rosenzweig-MacArthur prey-predator model with a degenerate noise, whereby only the prey variable is subject to small environmental fluctuations. This model has already been introduced in…
We study analytically, in one dimension, the survival probability $P_{s}(t)$ up to time $t$ of an immobile target surrounded by mutually noninteracting traps each performing a continuous-time random walk (CTRW) in continuous space. We…
We theoretically explore the possibility of sausage instabilities developing on top of a kink instability in lengthening current-carrying magnetic flux tubes. Observations indicate that the dynamics of magnetic flux tubes in our cosmos and…