arXiv subjects

Pedro Córdoba-Torres

Publications and source records attributed to Pedro Córdoba-Torres.

6 recordsLinked to original sources

arXiv2026

Emergent correlations in the selected link-times along optimal paths

In the context of first-passage percolation (FPP), we investigate the statistical properties of the selected link-times (SLTs) -the random link times comprising the optimal paths (or geodesics) connecting two given points. We focus on weakly disordered square lattices, whose geodesics are known to fall under the Kardar-Parisi-Zhang (KPZ) universality class. Our analysis reveals universal power-law decays with the end-to-end distance for both the average and standard deviation of the SLTs, along with an intricate pattern of long-range correlations, whose scaling exponents are directly linked to KPZ universality. Crucially, the SLT distributions for diagonal and axial paths exhibit significant differences, which we trace back to the distinct directed and undirected nature, respectively, of the underlying geodesics. Moreover, we demonstrate that the SLT distribution violates the conditions of the central limit theorem. Instead, SLT sums follow the Tracy-Widom distribution characteristic of the KPZ class, which we associate with evidence for the emergence of high-order long-range correlations in the ensemble.

cond-mat.stat-mech↗

arXiv2024

Unified theory for the scaling of the crossover between strong and weak disorder behaviors of optimal paths and directed/undirected polymers in disordered media

In this work we are concerned with the crossover between strong disorder (SD) and weak disorder (WD) behaviors in three well-known problems that involve minimal paths: directed polymers (directed paths with fixed starting point and length), optimal paths (undirected paths with fixed end-to-end/spanning distance) and undirected polymers (undirected paths with fixed starting point and length). We present a unified theoretical framework from which we can easily deduce the scaling of the crossover point of each problem. Our theory is based on the fact that the SD limit behavior of these systems is closely related to the corresponding percolation problem. As a result, the properties of those minimal paths are completely controlled by the so-called red bonds of percolation theory. Our model is first addressed numerically and then approximated by a ``two-term'' approach. This approach provides us with an analytical expression that seems to be reasonably accurate. The results are in perfect agreement with our simulations and with most of the results reported in related works. Our research also lead us to propose this crossover point as a universal measure of the disorder strength in each case. Interestingly, that measure depends on both the statistical properties of the disorder and the topological properties of the network.

cond-mat.stat-mech↗

arXiv2024

A unified scaling for the optimal path length in disordered lattices

In recent decades, much attention has been focused on the topic of optimal paths in weighted networks due to its broad scientific interest and technological applications. In this work we revisit the problem of the optimal path between two points and focus on the role of the geometry (size and shape) of the embedding lattice, which has received very little attention. This role becomes crucial, for example, in the strong disorder limit, where the mean length of the optimal path for a fixed end-to-end distance diverges as the lattice size increases. We propose a unified scaling ansatz for the mean length of the optimal path in $D-$dimensional disordered lattices. The ansatz is supported by a comprehensive numerical study of the problem on $2D$ lattices, yet we also present results in $D=3$. We show that it unifies well-known results in the strong and weak disorder regimes, including the crossover behavior, but it also reveals novel scaling scenarios not yet addressed. Moreover, it provides relevant insights into the origin of the universal exponents that characterize the scaling of the optimal path in the strong disorder limit.

cond-mat.stat-mech↗

arXiv2023

Shape effects in the fluctuations of random isochrones on a square lattice

We consider the isochrone curves in first-passage percolation on a 2D square lattice, i.e. the boundary of the set of points which can be reached in less than a given time from a certain origin. The occurrence of an instantaneous average shape is described in terms of its Fourier components, highlighting a crossover between a diamond and a circular geometry as the noise level is increased. Generally, these isochrones can be understood as fluctuating interfaces with an inhomogeneous local width which reveals the underlying lattice structure. We show that once these inhomogeneities have been taken into account, the fluctuations fall into the Kardar-Parisi-Zhang (KPZ) universality class with very good accuracy, where they reproduce the Family-Vicsek Ansatz with the expected exponents and the Tracy-Widom histogram for the local radial fluctuations.

cond-mat.stat-mech↗

arXiv2019

First-Passage Percolation under extreme disorder: from bond-percolation to Kardar-Parisi-Zhang universality

We consider the statistical properties of arrival times and balls on first-passage percolation (FPP) $2D$ square lattices with strong disorder in the link-times. A previous work showed a crossover in the weak disorder regime, between Gaussian and Kardar-Parisi-Zhang (KPZ) universality, with the crossover length decreasing as the noise amplitude grows. On the other hand, this work presents a very different behavior in the strong-disorder regime. A new crossover length appears below which the model is described by bond-percolation universality class. This characteristic length scale grows with the noise amplitude and diverges at the infinite-disorder limit. We provide a thorough characterization of the bond-percolation phase, reproducing its associated critical exponents through a careful scaling analysis of the balls. This is carried out through to a continuous mapping of the FPP passage time into the occupation probability of the bond-percolation problem. Moreover, the crossover length can be explained merely in terms of properties of the link-time distribution. The interplay between the new characteristic length and the correlation length intrinsic to bond-percolation determines the crossover between the initial percolation-like growth and theasymptotic KPZ scaling.

cond-mat.stat-mech↗

arXiv2018

Kardar-Parisi-Zhang Universality in First-Passage Percolation: the Role of Geodesic Degeneracy

We have characterized the scaling behavior of the first-passage percolation (FPP) model on two types of discrete networks, the regular square lattice and the disordered Delaunay lattice, thereby addressing the effect of the underlying topology. Several distribution functions for the link-times were considered. The asymptotic behavior of the fluctuations for both the minimal arrival time and the lateral deviation of the geodesic path are in perfect agreement with the Kardar-Parisi-Zhang (KPZ) universality class regardless of the type of the link-time distribution and of the lattice topology. Pre-asymptotic behavior, on the other hand, is found to depend on the uniqueness of geodesics in absence of disorder in the local crossing times, a topological property of lattice directions that we term geodesic degeneracy. This property has important consequences on the model, as for example the well-known anisotropic growth in regular lattices. In this work we provide a framework to understand its effect as well as to characterize its extent.

cond-mat.stat-mech↗