# Adriana NeumannUniversidade Federal do Rio Grande do Sul | UFRGS

Adriana Neumann

PhD

## About

48

Publications

4,830

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977

Citations

Introduction

Additional affiliations

April 2012 - present

Education

March 2007 - May 2011

## Publications

Publications (48)

Consider the semi-flow given by the continuous time shift \(\Theta _t:{\mathcal {D}} \rightarrow {\mathcal {D}} \), \(t \ge 0\), acting on the \({\mathcal {D}} \) of càdlàg paths (right continuous with left limits) \(w: [0,\infty ) \rightarrow S^1\), where \(S^1\) is the unitary circle (one can also take [0, 1] instead of \(S^1\)). We equip the spa...

Consider the semi-flow given by the continuous time shift $\Theta_t:\mathcal{D} \to \mathcal{D} $, $t \geq 0$, acting on the Skorokhod space $\mathcal{D} $, of paths $w: [0,\infty) \to S^1$, where $S^1$ is the unitary circle We show that the semi-flow is expanding. We consider a stochastic semi-group $e^{t\, L}$, $t \geq 0,$ where $L$ (the infinite...

We consider a Riemmaniann compact manifold $M$, the associated Laplacian $\Delta$ and the corresponding Brownian motion $X_t$, $t\geq 0.$ Given a Lipschitz function $V:M\to\mathbb R$ we consider the operator $\frac{1}{2}\Delta+V$, which acts on differentiable functions $f: M\to\mathbb R$ via the operator $$\frac{1}{2} \Delta f(x)+\,V(x)f(x) ,$$ for...

In this article, we consider a one-dimensional symmetric exclusion process in weak contact with reservoirs at the boundary. In the diffusive time-scaling the empirical measure evolves according to the heat equation with Robin boundary conditions. We prove the associated dynamical large deviations principle.

We study the convergence of the weak solution of the porous medium equation with a type of Robin boundary conditions, by tuning a parameter either to zero or to infinity. The convergence is in the strong sense, with respect to the L ² -norm, and the limiting function solves the same equation with Neumann (resp. Dirichlet) boundary conditions when t...

From the onset of the COVID-19 pandemic, we expected that people, especially women, caring for children, elderly, people with disabilities or other family members, would be the most impacted in academia; data proved this to be the case. This issue is central to the long-standing problem of low female representation in science, since women across al...

We prove a large deviations principle for the empirical measure of the one dimensional symmetric simple exclusion process in contact with reservoirs. The dynamics of the reservoirs is slowed down with respect to the dynamics of the system, that is, the rate at which the system exchanges particles with the boundary reservoirs is of order $n^{-\theta...

We study the asymptotic behaviour of the symmetric zero-range process in the finite lattice \(\{1,\ldots , N-1\}\) with slow boundary, in which particles are created at site 1 or annihilated at site \(N\!-\!1\) with rate proportional to \(N^{-\theta }\), for \(\theta \ge 1\). We present the invariant measure for this model and obtain the hydrostati...

The coronavirus disease 2019 (COVID-19) pandemic is altering dynamics in academia, and people juggling remote work and domestic demands – including childcare – have felt impacts on their productivity. Female authors have faced a decrease in paper submission rates since the beginning of the pandemic period. The reasons for this decline in women’s pr...

We study the convergence of the weak solution of the porous medium equation with a type of Robin boundary conditions, by tuning a parameter either to zero or to infinity. The convergence is in the strong sense, with respect to the $L^2$-norm, and the limiting function solves the same equation with Neumann (resp. Dirichlet) boundary conditions when...

While the Coronavirus disease 2019 (COVID-19) pandemic is altering academia dynamics, those juggling remote work and domestic demands, including childcare, have already felt the impacts on productivity. Female authors are facing a decrease in papers submission rates since the beginning of the pandemic period. The reasons for this decline in women p...

We study the asymptotic behaviour of the symmetric zero-range process in the finite lattice $\{1,\ldots, N-1\}$ with slow boundary, in which particles are created at site $1$ or annihilated at site $N\!-\!1$ with rate proportional to $N^{-\theta}$, for $\theta\geq 1$. We present the invariant measure for this model and obtain the hydrostatic limit....

We prove the non-equilibrium fluctuations for the one-dimensional symmetric simple exclusion process with a slow bond. This generalizes a result of [Stochastic Process. Appl. 123 (2013) 4156–4185; Stochastic Process. Appl. 126 (2016) 3235– 3242], which dealt with the equilibrium fluctuations. The foundation stone of our proof is a precise estimate...

We analyze the hydrodynamic behavior of the porous medium model (PMM) in a discrete space \(\{0,\ldots , n\}\), where the sites 0 and n stand for reservoirs. Our strategy relies on the entropy method of Guo et al. (Commun Math Phys 118:31–59, 1988). However, this method cannot be straightforwardly applied, since there are configurations that do not...

We derive the non-equilibrium fluctuations of one-dimensional symmetric simple exclusion processes in contact with stochastic reservoirs which are regulated by a factor n−θ. Depending on the range of θ we obtain processes with various boundary conditions. Moreover, as a consequence of the previous result, we deduce the non-equilibrium stationary fl...

We analyze the hydrodynamic behavior of the porous medium model in a discrete space $\{0,\ldots, n\}$, where the sites $0$ and $n$ stand for reservoirs. Our strategy relies on the entropy method of Guo, Papanicolau and Varadhan. However, this method cannot be straightforwardly applied, since there are configurations that do not evolve according to...

We derive the non-equilibrium fluctuations of one-dimensional symmetric simple exclusion processes in contact with slowed stochastic reservoirs which are regulated by a factor $n^{-\theta}$. Depending on the range of $\theta$ we obtain processes with various boundary conditions. Moreover, as a consequence of the previous result we deduce the non-eq...

We prove the non-equilibrium fluctuations for the one-dimensional symmetric simple exclusion process with a slow bond. This generalizes a result of T. Franco, A. Neumann and P. Gon\c{c}alves (2013), which dealt with the equilibrium fluctuations. The foundation stone of our proof is a precise estimate on the correlations of the system, and that is b...

We analyse the hydrodynamic limit of the porous medium model in contact with slow reservoirs which is given by a porous medium equation with Dirichlet, Robin or Neumann boundary conditions depending on the range of the parameter that rules the slowness of the reservoirs.

We prove that the equilibrium density fluctuations of the symmetric simple exclusion process in contact with slow boundaries is given by an Ornstein–Uhlenbeck process with Dirichlet, Robin or Neumann boundary conditions depending on the range of the parameter that rules the slowness of the boundaries.

We present the hydrodynamic and hydrostatic behavior of the Simple Symmetric
Exclusion Process with slow boundary. The slow boundary means that particles
can be born or die only at the boundary with rate proportional to
$N^{-\theta}$, where $\theta \geq 0$ and $N$ is the scale parameter, while in
the bulk the particles exchange rate is equal to $1$...

We prove that the equilibrium fluctuations of the symmetric simple exclusion process in contact with slow boundaries is given by an Ornstein-Uhlenbeck process with Dirichlet, Robin or Neumann boundary conditions depending on the range of the parameter that rules the slowness of the boundaries.

We consider a one-dimensional symmetric simple exclusion process in contact with slowed reservoirs: at the left (resp. right) boundary, particles are either created or removed at rates given by $\alpha/n$ or $(1-\alpha)/n$ (resp. $\beta/n$ or $(1-\beta)/n$) where $\alpha, \beta>0$ and $n$ is a scaling parameter. We obtain the non-equilibrium fluctu...

We present the correct space of test functions for the Ornstein–Uhlenbeck processes defined in Franco et al. (2013). Under these new spaces, an invariance with respect to a second order operator is shown, granting the existence and uniqueness of those processes. Moreover, we detail how to prove some properties of the semigroups, which are required...

We discuss here the hydrodynamic limit of independent quantum random walks evolving on \(\mathbb {Z}\). As main result, we obtain that the time evolution of the local equilibrium is governed by the convolution of the chosen initial profile with a rescaled version of the limiting probability density obtained in the law of large numbers for a single...

We consider the one-dimensional symmetric simple exclusion process with a
slow bond. In this model, whilst all the transition rates are equal to one, a
particular bond, the \emph{slow bond}, has associated transition rate of value
$N^{-1}$, where $N$ is the scaling parameter. This model has been considered in
previous works on the subject of hydrod...

We consider a family of continuous time symmetric random walks indexed by
$k\in \mathbb{N}$, $\{X_k(t),\,t\geq 0\}$. For each $k\in \mathbb{N}$ the
matching random walk take values in the finite set of states
$\Gamma_k=\frac{1}{k}(\mathbb{Z}/k\mathbb{Z})$ which is a subset of the unitary
circle. The stationary probability for such process converges...

We obtain the fluctuations for the occupation time of one-dimensional
symmetric exclusion processes with speed change, where the transition rates
(conductances) are driven by a general function W. The approach does not
require sharp bounds on the spectral gap of the system nor the jump rates to be
bounded from above or below. We present some exampl...

This is a short survey on recent results obtained by the authors on dynamical
phase transitions of interacting particle systems. We consider particle systems
with exclusion dynamics, but it is conjectured that our results should hold for
a general class of particle systems. The parameter giving rise to the phase
transition is the "slowness" of a si...

We present a proof of the hydrodynamic limit of independent quantum random
walks evolving on Z.

Through this paper we analyze the ergodic properties of continuous time Markov chains with values on the one-dimensional spin lattice \(\{1,\dots,d\}^{{\mathbb{N}}}\) (also known as the Bernoulli space). Initially, we consider as the infinitesimal generator the operator
, where
is a discrete time Ruelle operator (transfer operator), and \(A:\{1,\do...

We analyze the equilibrium fluctuations of the density, current and tagged
particle in symmetric exclusion with a slow bond. The system evolves in the
one-dimensional lattice and the jump rate is everywhere equal to one except at
the slow bond where it is $\alpha n^-\beta$, where $\alpha,\beta\geq{0}$ and
$n$ is the scaling parameter. Depending on...

In this work, we present symmetric simple exclusion processes with a finite number of bonds whose dynamics is slowed down in order to difficult the passage of particles at those bonds. We study the influence of the rate of passage of mass at those bonds in the macroscopic hydrodynamic equation. As a consequence, we exhibit a dynamical phase transit...

We consider the exclusion process evolving in the one-dimensional discrete
torus, with a bond whose conductance slows down the passage of particles across
it. We chose the conductance at that bond as $\alpha n^{-\beta}$, where
$\alpha>0$, $\beta\in [0,\infty]$, and $n$ is the scale parameter. In
\cite{fgn}, by rescaling time diffusively, it was pro...

Let Λ be a connected closed region with smooth boundary contained in the
d-dimensional continuous torus Td. In the
discrete torus
N-1TdN, we
consider a nearest-neighbor symmetric exclusion process where occupancies of
neighboring sites are exchanged at rates depending on Λ in the following
way: if both sites are in Λ or Λc, the exchange rate
is 1;...

Let Λ be a connected closed region with smooth boundary contained in the d-dimensional continuous torus T
d
. In the discrete torus N-1T
d
N
, we consider a nearest-neighbor symmetric exclusion process where occupancies of neighboring sites are exchanged at rates depending on Λ in the following way: if both sites are in Λ or Λc, the exchange rate...

We consider the exclusion process in the one-dimensional discrete torus with
$N$ points, where all the bonds have conductance one, except a finite number of
slow bonds, with conductance $N^{-\beta}$, with $\beta\in[0,\infty)$. We prove
that the time evolution of the empirical density of particles, in the diffusive
scaling, has a distinct behavior a...

Let $\Lambda$ be a connected closed region with smooth boundary contained in the $d$-dimensional continuous torus $\bb T^d$. In the discrete torus $N^{-1} \bb T^d_N$, we consider a nearest neighbor symmetric exclusion process where occupancies of neighboring sites are exchanged at rates depending on $\Lambda$ in the following way: if both sites are...

Neste artigo são construídas, de forma concreta, transformações con-formes de algumas regiões duplamente conexas em anel. Para isso utilizamos as funções elementares e suas propriedades, os princípios básicos das transformações conformes, o princípio de simetria de Riemann-Schwarz e a integral de Schwarz-Christoffel.