Related papers: Some recent progress on the stationary measure for…
In this work we focus on the two-dimensional anisotropic KPZ (aKPZ) equation, which is formally given by \begin{equation*}\partial_t h =\frac{\nu}{2}\Delta h + \lambda((\partial_1 h)^2 - (\partial_2 h)^2) +…
Let $\mu_N$ be the empirical measure associated to a $N$-sample of a given probability distribution $\mu$ on $\mathbb{R}^d$. We are interested in the rate of convergence of $\mu_N$ to $\mu$, when measured in the Wasserstein distance of…
The PWP method was introduced by Diaz in 2009 as a technique for measuring indirect influences in complex networks. It depends on a matrix D, provided by the user, called the matrix of direct influences, and on a positive real parameter…
On a closed manifold, consider the space of all Riemannian metrics for which -Delta + kR is positive (nonnegative) definite, where k > 0 and R is the scalar curvature. This spectral generalization of positive (nonnegative) scalar curvature…
Motivated by recent experimental activities on surface critical phenomena, we present a detailed theoretical study of the near-surface behavior of the local order parameter m(z) in Ising-like spin systems. Special attention is paid to the…
We consider generalizations of open ASEP in the interval and half-space, where the speed of the reservoir dynamics can depend on the local particle configuration. We show that their height functions have a continuum limit given by the open…
An overview of recent studies of nonequilibrium bound interfaces is given. Attention is focused on Kardar-Parisi-Zhang interfaces in the presence of upper and lower walls, interacting via short-- and long--ranged potentials. A comparison…
This article discusses two recent works by the author, one with Brown and Hurtado on Zimmer's conjecture and one with Bader, Miller and Stover on totally geodesic submanifolds of real and complex hyperbolic manifolds. The main purpose of…
We study a $(2+1)$-dimensional stochastic interface growth model, that is believed to belong to the so-called Anisotropic KPZ (AKPZ) universality class [Borodin and Ferrari, 2014]. It can be seen either as a two-dimensional interacting…
We study the critical behavior of the nonequilibrium dynamics and of the steady states emerging from the competition between coherent and dissipative dynamics close to quantum phase transitions. The latter is induced by the coupling of the…
This paper is partly an exposition, and partly an extension of our work [1] to the multiparameter case. We consider certain classes of parametrized dynamically defined measures. These are push-forwards, under the natural projection, of…
We present a comprehensive numerical investigation of non-universal parameters and corrections related to interface fluctuations of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class, in d=1+1, for both flat and curved…
The celebrated results of Koml\'os, Major and Tusn\'ady [Z. Wahrsch. Verw. Gebiete 32 (1975) 111-131; Z. Wahrsch. Verw. Gebiete 34 (1976) 33-58] give optimal Wiener approximation for the partial sums of i.i.d. random variables and provide a…
This article investigates stationary surfaces with boundaries, which arise as the critical points of functionals dependent on curvature. Precisely, a generalized "bending energy" functional $\mathcal{W}$ is considered which involves a…
We consider the Kardar-Parisi-Zhang (KPZ) equation for a circular interface in two dimensions, unconstrained by the standard small-slopes and no-overhang approximations. Numerical simulations using an adaptive scheme allow us to elucidate…
Using the Lindblad equation approach, we derive the range of the parameters of an interacting one-dimensional electronic chain connected to two reservoirs in the large bias limit in which an optimal working point (corresponding to a change…
Studying sample path behaviour of stochastic fields/processes is a classical research topic in probability theory and related areas such as fractal geometry. To this end, many methods have been developed since a long time in Gaussian…
A crystal surface which is miscut with respect to a high symmetry plane exhibits steps with a characteristic distance. It is argued that the continuum description of growth on such a surface, when desorption can be neglected, is given by…
An unbounded one-dimensional solid-on-solid model with integer heights is studied. Unbounded here means that there is no a priori restrictions on the discret e gradient of the interface. The interaction Hamiltonian of the interface is given…
We analyse the so-called small-world network model (originally devised by Strogatz and Watts), treating it, among other things, as a case study of non-linear coupled difference or differential equations. We derive a system of evolution…