arXiv subjects

Sergio I. López

Publications and source records attributed to Sergio I. López.

7 recordsLinked to original sources

arXiv2026

Abrupt decorrelation for linear stochastic differential equations

Understanding how a system loses memory of its initial state is a central problem in probability and statistics. In this manuscript, we introduce the notion of abrupt decorrelation, which explicitly characterises a sharp and sudden loss of correlation over time. We study this phenomenon within a class of linear stochastic differential equations (LSDEs), where explicit descriptions are available under various statistical distances. Our main focus is on the multivariate Ornstein-Uhlenbeck process, while in the one-dimensional case we extend the analysis to LSDEs with time-dependent drifts. The results highlight strong parallels with the cut-off phenomenon in Markov processes and contribute to a broader understanding of decorrelation in stochastic systems.

math.PR↗

arXiv2025

A degree-biased cutting process for random recursive trees

We investigate a degree-biased cutting process on random recursive trees, where each vertex is deleted with probability proportional to its degree. We establish the splitting property and derive the explicit distribution of the number of vertices deleted in each cut. This leads to a recursive formula for Kn, the number of cuts needed to erase a random recursive tree with n vertices. Furthermore, we show that Kn is stochastically dominated by Jn, the number of jumps made by a related walk with a barrier. We prove that Jn converges in distribution to a random variable with a spectrally negative stable distribution. Finally, we examine connections between this cutting procedure and a coalescing process on the set of n elements.

math.PR↗

arXiv2023

On the two-point function of the one-dimensional KPZ equation

In this short communication we show that basic tools from Malliavin calculus can be applied to derive the two-point function of the slope of the one-dimensional KPZ equation, starting from an arbitrary two-sided Brownian motion, in terms of the polymer end-point annealed distribution associated to the stochastic heat equation. We also prove that this distribution is given in terms of the derivative of the variance of the solution of the KPZ equation.

math.PR↗

arXiv2022

Targeted cutting of random recursive trees

We propose a method for cutting down a random recursive tree that focuses on its higher degree vertices. Enumerate the vertices of a random recursive tree of size $n$ according to a decreasing order of their degrees; namely, let $(v^{(i)})_{i=1}^{n}$ be so that $deg(v^{(1)}) \geq \cdots \geq deg (v^{(n)})$. The targeted, vertex-cutting process is performed by sequentially removing vertices $v^{(1)}$, $v^{(2)}, \ldots, v^{(n)}$ and keeping only the subtree containing the root after each removal. The algorithm ends when the root is picked to be removed. The total number of steps for this procedure, $X_n^{targ}$, is upper bounded by $Z_{\geq D}$, which denotes the number of vertices that have degree at least as large as the degree of the root. We obtain that the first order growth of $X_n^{targ}$ is upper bounded by $n^{1-\ln 2}$, which is substantially smaller than the required number of removals if, instead, the vertices where selected uniformly at random. More precisely, we prove that $\ln(Z_{\geq D})$ grows as $\ln(n)$ asymptotically and obtain its limiting behavior in probability. Moreover, we obtain that the $k$-th moment of $\ln(Z_{\geq D})$ is proportional to $(\ln(n))^k$.

math.PR↗

arXiv2021

Bus operators in competition: a directed location approach

We present a directed variant of Salop (1979) model to analyze bus transport dynamics. The players are operators competing in cooperative and non-cooperative games. Utility, like in most bus concession schemes in emerging countries, is proportional to the total fare collection. Competition for picking up passengers leads to well documented and dangerous driving practices that cause road accidents, traffic congestion and pollution. We obtain theoretical results that support the existence and implementation of such practices, and give a qualitative description of how they come to occur. In addition, our results allow to compare the current or base transport system with a more cooperative one.

econ.TH↗

arXiv2016

On the location of the maximum of a process: Lévy, Gaussian and multidimensional cases

In this short article we show how the techniques presented in arXiv:1207.4469 can be extended to a variety of non continuous and multivariate processes. As examples, we prove uniqueness of the location of the maximum for spectrally positive Lévy processes, Ornstein-Uhlenbeck process, fractional Brownian Motion and the Brownian sheet among others gaussian processes.

math.PR↗

arXiv2014

Convergence of tandem Brownian queues

It is known that in a stationary Brownian queue with both arrival and service processes equal in law to Brownian motion, the departure process is a Brownian motion, that is, Burke's theorem in this context. In this short note we prove convergence to this invariant measure: if we have an arbitrary continuous process satisfying some mild conditions as initial arrival process and pass it through an infinite tandem network of queues, the resulting process weakly converges to a Brownian motion. We assume independent and exponential initial workloads for all queues.

math.PR↗