Mixing of the Averaging process and its discrete dual on finite-dimensional geometries

We analyze the $L^1$-mixing of a generalization of the Averaging process introduced by Aldous. The process takes place on a growing sequence of graphs which we assume to be finite-dimensional, in the sense that the random walk on those geometries satisfies a family of Nash inequalities. As a byproduct of our analysis, we provide a complete picture of the total variation mixing of a discrete dual of the Averaging process, which we call Binomial Splitting process. A single particle of this process is essentially the random walk on the underlying graph. When several particles evolve together, they interact by synchronizing their jumps when placed on neighboring sites. We show that, given $k$ the number of particles and $n$ the (growing) size of the underlying graph, the system exhibits cutoff in total variation if $k\to\infty$ and $k=O(n^2)$. Finally, we exploit the duality between the two processes to show that the Binomial Splitting satisfies a version of Aldous' spectral gap identity, namely, the relaxation time of the process is independent of the number of particles.Comment: 30 pages. Typos fixe

Spectral gap of the symmetric inclusion process

We consider the symmetric inclusion process on a general finite graph. Our main result establishes universal upper and lower bounds for the spectral gap of this interacting particle system in terms of the spectral gap of the random walk on the same graph. In the regime in which the gamma-like reversible measures of the particle systems are log-concave, our bounds match, yielding a version for the symmetric inclusion process of the celebrated Aldous' spectral gap conjecture originally formulated for the interchange process. Finally, by means of duality techniques, we draw analogous conclusions for an interacting diffusion-like unbounded conservative spin system known as Brownian energy process.Comment: 16 page

Stochastic duality and eigenfunctions

We start from the observation that, anytime two Markov generators share an eigenvalue, the function constructed from the product of the two eigenfunctions associated to this common eigenvalue is a duality function. We push further this observation and provide a full characterization of duality relations in terms of spectral decompositions of the generators for finite state space Markov processes. Moreover, we study and revisit some well-known instances of duality, such as Siegmund duality, and extract spectral information from it. Next, we use the same formalism to construct all duality functions for some solvable examples, i.e., processes for which the eigenfunctions of the generator are explicitly known

Higher order hydrodynamics and equilibrium fluctuations of interacting particle systems

Motivated by the recent preprint [arXiv:2004.08412] by Ayala, Carinci, and Redig, we first provide a general framework for the study of scaling limits of higher order fields. Then, by considering the same class of infinite interacting particle systems as in [arXiv:2004.08412], namely symmetric simple exclusion and inclusion processes in the d-dimensional Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium fluctuations, of higher order fields. In particular, the limit fields exhibit a tensor structure. Our fluctuation result differs from that in [arXiv:2004.08412], since we consider a different notion of higher order fluctuation fields.Comment: 29 pages, to appear in Markov Process. Related Field

Productividad de la rotación anual raigrás- maíz en galicia: evaluación durante cinco años en regadío y secano y bajo dos sistemas de siembra

Es un estudio sobre la productividad de la rotación anual raigrás- maíz en galicia: evaluación durante cinco años en regadío y secano y bajo dos sistemas de siembr

Hydrodynamics for the partial exclusion process in random environment

In this paper, we introduce a random environment for the exclusion process in $\Z^d$ obtained by assigning a maximal occupancy to each site. This maximal occupancy is allowed to randomly vary among sites, and partial exclusion occurs. Under the assumption of ergodicity under translation and uniform ellipticity of the environment, we derive a quenched hydrodynamic limit in path space by strengthening the mild solution approach initiated in \cite{nagy_symmetric_2002} and \cite{faggionato_bulk_2007}. To this purpose, we prove, employing the technology developed for the random conductance model, a homogenization result in the form of an arbitrary starting point quenched invariance principle for a single particle in the same environment, which is a result of independent interest. The self-duality property of the partial exclusion process allows us to transfer this homogenization result to the particle system and, then, apply the tightness criterion in \cite{redig_symmetric_2018}

Symmetric inclusion process with slow boundary: hydrodynamics and hydrostatics

We study the hydrodynamic and hydrostatic limits of the one-dimensional open symmetric inclusion process with slow boundary. Depending on the value of the parameter tuning the interaction rate of the bulk of the system with the boundary, we obtain a linear heat equation with either Dirichlet, Robin or Neumann boundary conditions as hydrodynamic equation. In our approach, we combine duality and first-second class particle techniques to reduce the scaling limit of the inclusion process to the limiting behavior of a single, non-interacting, particle.Comment: 35 pages, 1 figure. Final version. To appear in Bernoull

Predicción de la fenología de vicia faba l.: estimación de parámetros con el modelo cropgro- faba bean usando experimentos de múltiples fechas de siembra.

Entre los modelos de leguminosas más mecanicistas se puede destacar el modelo CROPGRO. Boote et al. (2002) adaptaron el CROPGRO para simular el crecimiento del haba (Vicia faba L.), naciendo así, CROPGRO-faba bean (incluido en el paquete DSSAT V4) en el que la tasa de desarrollo se expresa como día fisiológico (DF) transcurrido por día del calendario (día) (Ec. 1) y es una función multiplicativa de la temperatura (T) y fotoperíodo (P). Cada una de estas funciones adopta valores comprendidos entre 0 y