Noticias en español
Diameter and mixing time of the giant component in the percolated hypercube.
Resumen: The d-dimensional binary hypercube is the graph whose vertices represent the binary vectors of length d and two vertices are adjacent if they differ in a single coordinate. The percolated hypercube (where every edge is retained independently with probability p) is a classic model in random graph theory. In this talk, we are going to survey some of the history of the model and discuss recent estimates of the mixing time of the lazy simple random walk and the diameter of the giant component in a supercritical percolated hypercube. Based on a joint work with Michael Anastos, Sahar...
Read MoreDrift parameter estimation for a fractional interacting particle system.
Resumen: We consider a system of interacting particles with Lipschitz continuous drift functions, driven by additive fractional Brownian motions with H in [1/2, 1). For this system, we address the drift parameter estimation problem from continuous observations over a fixed time interval, assuming that the drift depends linearly on an unknown parameter vector. We propose estimators inspired by the least squares approach, demonstrate their consistency and asymptotic normality as the number of particles tends to infinity, and present a numerical study illustrating our findings. The proofs rely...
Read MoreRecent advances on multiple ergodic averages
RESUMEN In 1977, Furstenberg gave a dynamical proof of the theorem of Szemerédi on the existence of arithmetic progressions in dense subsets of integers. In doing so, he initiated the use of ergodic methods to solve problems originating from additive combinatorics and number theory. A central object of study in this field are multiple ergodic averages, a class of multilinear operators that generalize classical Birkhoff averages and can be used to count the number of arithmetic patterns in dense sets of integers. In this talk, I will outline the history of multiple ergodic averages, with...
Read MoreSingle orbits and Wiener-Wintner theorem
RESUMEN A single-orbit approach to dynamics links the global properties of a dynamical system with the behaviour of its orbits. During the talk, I shall discuss what can be deduced about the system from the existence of an orbit satisfying the conclusion of the Wiener-Wintner theorem (a Wiener-Wintner generic orbit). I will examine the spectrum of ergodic measures by examining the behaviour of their Wiener–Wintner generic points. Moreover, by investigating the properties of a “regular” subclass of such points, I shall characterise ergodic measures with discrete...
Read MoreDistribution Modulo 1 and Applications
Abstract: In this work, we present an overview of fundamental results in the theory of uniform distribution modulo 1 and the closely related field of discrepancy theory. After introducing the main concepts, tools, and classical theorems, we explore how these ideas can be applied to problems arising in dynamical systems and fractal analysis. In particular, we discuss their role in understanding the spectral properties of substitution dynamical systems and in the study of Bernoulli convolutions.
Read MorePlanning Deeply Decarbonized Power Systems
Abstract: The energy transition is reshaping power system planning and operation as renewable penetration increases and electrification expands into sectors such as heating and cooling, making systems more dependent on weather-driven variability and uncertainty. Addressing these challenges requires models that can capture both short-term operational flexibility and long-term uncertainty, supported by suitable solution methods. This presentation examines the challenges of long-term power system planning under uncertainty in the context of the energy transition and explores the use of...
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