Ionel Popescu
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Ionel Popescu has a total of 6 co-authors. Here are the top co-authors by number of shared publications:
- Arghir Zarnescu
Basque Center for Applied Mathematics, Mazarredo 14, E48009 Bilbao, Bizkaia, Spain
1 shared publication - Iulian Cîmpean
Faculty of Mathematics and Computer Science University of Bucharest 14 Academiei str. 70109 Bucharest Romania
1 shared publication - Lucas Babet1 shared publication
- Lucian Beznea
Simion Stoilow Institute of Mathematics Romanian Academy Research unit No 2 P.O. Box 1-764 RO-014700 Bucharest Romania
1 shared publication - Oana Lupascu-Stamate
Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy "Gheorghe Mihoc -Caius Iacob" 13 Calea 13 Septembrie 050711 Bucharest Romania
1 shared publication - Tushar Vaidya
School of Physical and Mathematical Sciences Nanyang Technological University Singapore
1 shared publication
Latest Publications
- Open Access
Tridiagonal random matrices, an analytic approach
In this paper, we study the limiting distribution of the eigenvalues for random tridiagonal matrix models. The limiting distribution is well described by its moments. Here, an analytical approach allows us, as in the case of Wigner matrices, to relax the assumptions on the random variables. With this method, we proved the convergence of the spectral distribution under an assumption on the second moment. We discuss also about an algebraic approach for the tridiagonal models, which are more complicated than the classic freeness.
Open AccessTridiagonal random matrices, an analytic approach
In this paper, we study the limiting distribution of the eigenvalues for random tridiagonal matrix models. The limiting distribution is well described by its moments. Here, an analytical approach allows us, as in the case of Wigner matrices, to relax the assumptions on the random variables. With this method, we proved the convergence of the spectral distribution under an assumption on the second moment. We discuss also about an algebraic approach for the tridiagonal models, which are more complicated than the classic freeness.
- Open Access
From Monte Carlo to neural networks approximations of boundary value problems
In this paper we study probabilistic and neural network approximations for solutions to Poisson equation subject to H\" older data in general bounded domains of $\mathbb{R}^d$. We aim at two fundamental goals. The first, and the most important, we show that the solution to Poisson equation can be numerically approximated in the sup-norm by Monte Carlo methods, { and that this can be done highly efficiently if we use a modified version} of the walk on spheres algorithm { as an acceleration method. This provides estimates which are efficient with respect to the prescribed approximation error and with polynomial complexity in the dimension and the reciprocal of the error.} {A crucial feature is that} the overall number of samples does not not depend on the point at which the approximation is performed. As a second goal, we show that the obtained Monte Carlo solver renders { in a constructive way} ReLU deep neural network (DNN) solutions to Poisson problem, whose sizes depend at most polynomialy in the dimension $d$ and in the desired error. In fact we show that the random DNN provides with high probability a small approximation error and low polynomial complexity in the dimension.Open AccessFrom Monte Carlo to neural networks approximations of boundary value problems
In this paper we study probabilistic and neural network approximations for solutions to Poisson equation subject to H\" older data in general bounded domains of $\mathbb{R}^d$. We aim at two fundamental goals. The first, and the most important, we show that the solution to Poisson equation can be numerically approximated in the sup-norm by Monte Carlo methods, { and that this can be done highly efficiently if we use a modified version} of the walk on spheres algorithm { as an acceleration method. This provides estimates which are efficient with respect to the prescribed approximation error and with polynomial complexity in the dimension and the reciprocal of the error.} {A crucial feature is that} the overall number of samples does not not depend on the point at which the approximation is performed. As a second goal, we show that the obtained Monte Carlo solver renders { in a constructive way} ReLU deep neural network (DNN) solutions to Poisson problem, whose sizes depend at most polynomialy in the dimension $d$ and in the desired error. In fact we show that the random DNN provides with high probability a small approximation error and low polynomial complexity in the dimension. - Open Access
Averaging plus Learning Models and Their Asymptotics
We develop original models to study interacting agents in financial markets and in social networks. Within these models randomness is vital as a form of shock or news that decays with time. Agents learn from their observations and learning ability to interpret news or private information in time-varying networks. Under general assumption on the noise, a limit theorem is developed for the generalised DeGroot framework for certain type of conditions governing the learning. In this context, the agents beliefs (properly scaled) converge in distribution that is not necessarily normal. Fresh insights are gained not only from proposing a new setting for social learning models but also from using different techniques to study discrete time random linear dynamical systems.
Open AccessAveraging plus Learning Models and Their Asymptotics
We develop original models to study interacting agents in financial markets and in social networks. Within these models randomness is vital as a form of shock or news that decays with time. Agents learn from their observations and learning ability to interpret news or private information in time-varying networks. Under general assumption on the noise, a limit theorem is developed for the generalised DeGroot framework for certain type of conditions governing the learning. In this context, the agents beliefs (properly scaled) converge in distribution that is not necessarily normal. Fresh insights are gained not only from proposing a new setting for social learning models but also from using different techniques to study discrete time random linear dynamical systems.