Related papers: Some recent progress on the stationary measure for…
The short-time evolution of a growing interface is studied analytically and numerically for the Kadar-Parisi-Zhang (KPZ) universality class. The scaling behavior of response and correlation functions is reminiscent of the ``initial slip''…
We prove relativistic versions of the ladder asymptotics from V. Guillemin and A. Uribe [Journal of Differential Geometry, 32(2):315-347, 1990] on principal bundles over globally hyperbolic, stationary, spatially compact spacetimes equipped…
A compactification of the E_8 x E_8 heterotic string on a Z_2 x Z_2 orbifold equipped with an additional freely acting involution is presented. This model reproduces the exact chiral MSSM spectrum with matter parity and a non-trivial Yukawa…
We examine an Unruh-DeWitt particle detector coupled to a scalar field in three-dimensional curved spacetime. We first obtain a regulator-free expression for the transition probability in an arbitrary Hadamard state, working within…
Simulations of restricted solid-on-solid growth models are used to build the width-distributions of d=2-5 dimensional KPZ interfaces. We find that the universal scaling function associated with the steady-state width-distribution changes…
Many models of one-dimensional local random growth are expected to lie in the Kardar-Parisi-Zhang (KPZ) universality class. For such a model, the interface profile at advanced time may be viewed in scaled coordinates specified via…
We study the quantum dynamics of many-body systems, in the presence of dissipation due to the interaction with the environment, under Kibble-Zurek (KZ) protocols in which one Hamiltonian parameter is slowly, and linearly in time, driven…
While adversarial robustness and generalization have individually received substantial attention in the recent literature on quantum machine learning, their interplay is much less explored. In this chapter, we address this interplay for…
We attempt to describe the moduli space of boundary states in the SU(2)$_k$ WZW model by constructing marginally deformed solutions in open string field theory in the level truncation approximation. In contrast with other approaches to…
The main subject of the thesis is the study of stationary nonequilibrium states trough the use of microscopic stochastic models that encode the physical interaction in the rules of Markovian dynamics for particles configurations. These…
We study the porous medium equation (PME) in one space dimension in presence of additive non-conservative white noise, and interpreted as a stochastic growth equation for the height field of an interface. We predict the values of the two…
Asymmetric exclusion process (TASEP) along a one-dimensional (1D) open channel sets the paradigm for 1D driven models and nonequilibrium phase transitions in open 1D models. Inspired by the phenomenologies of an open TASEP with Langmuir…
Recent experimental works on one-dimensional (1D) circular Kardar-Parisi-Zhang (KPZ) systems whose radii decrease in time have reported controversial conclusions about the statistics of their interfaces. Motivated by this, we investigate…
Growth of interfaces during vapor deposition is analyzed on a discrete lattice. It leads to finding distribution of local heights, measurable for any lattice model. Invariance in the change of this distribution in time is used to determine…
Triadic closure describes the tendency for new friendships to form between individuals who already have friends in common. It has been argued heuristically that the triadic closure effect can lead to bistability in the formation of…
This paper is inspired by the problem of understanding in a mathematical sense the Liouville quantum gravity on surfaces. Here we show how to define a stationary random metric on self-similar spaces which are the limit of nice finite…
We study the stochastic six-vertex model on a strip $$\left\{(x,y)\in\mathbb{Z}^2: 0\leq y\leq x\leq y+N\right\}$$ with two open boundaries. We develop a `matrix product ansatz' method to solve for its stationary measure, based on the…
We consider the continuous model of log-infinitely divisible multifractal random measures (MRM) introduced in \cite{bacry} . If M is a non degenerate multifractal measure with associated metric $\rho(x,y)=M([x,y])$ and structure function…
We study Markov interval maps with random holes. The holes are not necessarily elements of the Markov partition. Under a suitable, and physically relevant, assumption on the noise, we show that the transfer operator associated with the…
We propose a mean field theory for interfaces growing according to the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. The mean field equations are formulated in terms of densities at different heights, taking surface tension and the…