arXiv subjects

Ulysse Marquis

Publications and source records attributed to Ulysse Marquis.

10 recordsLinked to original sources

arXiv2026

Beyond dynamic scaling: rare events break universality

Surface growth driven by non-monomeric deposition has remained largely unexplored. We investigate a model based on the deposition of blobs with a power-law size distribution $P(s)\sim s^{-τ}$. We find that the critical exponents vary continuously with $τ$, recovering Kardar--Parisi--Zhang behavior only for $τ\ge 3$. For $τ<3$, roughness scaling exhibits strong corrections and scale invariance breaks down. We show that this behavior originates from the emergence of a second dynamical length scale $ζ$, corresponding to the linear size of the largest cluster, in addition to the usual correlation length $ξ$. The coexistence of these two relevant scales signals the breakdown of the usual Family--Vicsek scaling. These results point to a new phenomenology of surface growth beyond the standard scale-invariant paradigm.

cond-mat.stat-mech↗

arXiv2026

Invasion with size-dependent dispersion range

The coalescing colony model provides a minimal framework for biological invasions with long-range dispersion. In its standard formulation, the dispersion range is assumed independent of the size of the invading population. Here, we relax this assumption and consider size-dependent dispersal: a main colony of linear size $r$ emits secondary colonies at distance $r^μ$, with $0 \leq μ\leq 1$. We derive the generalized dynamical equations for this extended model and map out the growth phase diagram for the leading order contribution. Depending on $μ$, the main colony exhibits distinct regimes: linear expansion, power-law growth, exponential regime and finite-time blow-up. We confront these theoretical predictions with a spatially explicit physical model. While the coalescing colony approach correctly captures the scaling of the perimeter, it fails to predict the scaling of the volume. We trace this discrepancy to an effective breakdown of circular symmetry in the morphology of the main colony. Finally, we quantify temporal evolution of the population fraction residing outside of the main colony. The coalescing colony model predicts its decay to~$0$ like a power-law when~$μ<1$, and a macroscopic amount of the population remains in the secondary colonies at~$μ=1$. Simulations of the physical model reveal a persistent satellite population not captured by the theory at~$μ>μ^*\approx 0.7$. Broadly, our findings highlight how coupling dispersal range to population size fundamentally alters invasion dynamics, with implications for biological invasions, metastatic growth, and urban expansion.

q-bio.PE↗

arXiv2026

Spectral properties of non-Hermitian real random matrices with long-range correlations

We investigate the spectral properties of non-Hermitian real random matrices whose entries exhibit long-range correlations decaying as~$|r-r'|^{-α}$. We find a progressive breakdown of the circular law, controlled by the decrease of~$α$. In all cases, the radial eigenvalue density decreases away from the origin. At~$α>1$, an effective radius, reminiscent of the circular law, is retrieved, while instead, for~$α<1$, the eigenvalue distribution broadens with matrix size and its spectral radius grows like a power law, with exponents numerically close to the exponents controlling the magnitude of fluctuations in the extended central limit theorem. The case~$α=1$ appears as a case with self-similar eigenvalue density, and slowly growing spectral radius. Long-range correlations also enhance clustering of real eigenvalues and slow the resorption of the Saturn effect. These results reveal a correlation-driven transition and suggest the emergence of a new universality class for correlated non-Hermitian random matrices.

cond-mat.dis-nn↗

arXiv2026

On the Meaning of Urban Scaling

Cities are often compared through scaling laws, usually expressed as power-law relations between population size and aggregate urban quantities related to infrastructure, socioeconomic activity, or environmental impacts. These laws are influential because their exponent is often interpreted as describing what happens when a city grows, with implications for urban theory, planning, and policy. Here, we show that this interpretation is generally misleading. An exponent measured by comparing many cities at one date does not, in general, describe the trajectory of any individual city. Instead, it reflects a statistical pattern produced by cities with different histories, constraints, institutions, and growth paths. Apparent sublinear or superlinear scaling can therefore arise even when individual cities follow simpler dynamics, as we show for the area--population relation. Cross-sectional scaling laws can reveal system-level regularities, but should not be used alone to infer growth mechanisms or guide policy for a given city.

physics.soc-ph↗

arXiv2026

FKPP fronts in quenched random media

We study numerically the evolution of one-dimensional FKPP fronts initiated from steep initial conditions in the presence of a quenched random growth rate. Compared to both the homogeneous case (with velocity $v_0$) and deterministic disorder, quenched randomness increases the average propagation speed. We show that the velocity shift relative to the homogeneous case scales linearly with the disorder variance $σ^2$, with a universal prefactor -- independent of the specific distribution of the disorder -- such that $v = v_0 + a σ^2$, with $a \approx 0.02432 \pm 0.00002$. Moreover, the front position exhibits diffusive fluctuations across disorder realizations. The corresponding effective diffusion coefficient scales quadratically with $σ$, $D = \frac{b^2 σ^2}{2}$, with $b \approx 0.223 \pm 0.002$. These results suggest a universal statistical response of FKPP fronts to quenched heterogeneity.

cond-mat.dis-nn↗

arXiv2026

Modeling the spatial growth of cities

The growth of cities has traditionally been studied from a population perspective, while urban expansion-its spatial growth-has often been approached qualitatively. However, characterizing and modeling this spatial expansion is crucial, particularly given its parallels with surface growth extensively studied in physics. Despite these similarities, approaches to urban expansion modeling are fragmented and scattered across various disciplines and contexts. In this review, we provide a comprehensive overview of the mathematical modeling of this complex phenomenon. We discuss the key challenges hindering progress and examine models inspired by statistical physics, economics and geography, and theoretical ecology. Finally, we highlight critical directions for future research in this interdisciplinary field.

physics.soc-ph↗

arXiv2026

Mathematical modeling of urban sprawl

Urban land cover doubled between 1985 and 2015, yet the spatial dynamics of urban form remain under-quantified, despite its importance for sustainability, infrastructure planning, and climate risk. Urban expansion is a non-equilibrium process shaped by interactions between population growth, infrastructure, institutions, and market failures -- rendering static and equilibrium models inadequate. We review key challenges and modeling approaches, focusing on partial differential equation (PDE) frameworks. Borrowed from statistical physics, PDEs capture spatial heterogeneity, anisotropy, stochasticity, and feedbacks between land use and transport networks. Integrating economic and institutional factors remains a major challenge for policy relevance. We propose a research agenda that bridges remote sensing, urban economics, and complexity science to develop dynamic, empirically grounded models of urban expansion.

physics.soc-ph↗

arXiv2025

Diffusive geodesics wandering in networks of rigid chains

We introduce an ensemble of spatial networks built from the junctions of hindered-rotation chains, incorporating directional correlations between bonds, an aspect ignored in the standard network modeling paradigm. The emergent random networks support geodesics with a wandering exponent $ξ= 1/2$, and a travel-time fluctuation exponent $χ= 0$, consistent with the KPZ relation, yet violating the bound~$χ\geq1/8$ predicted in the Poissonian framework. Transverse deviations follow the Kolmogorov distribution, indicating similarities between Brownian bridge excursions and geodesics in a random medium with correlated edges orientations. These results reveal a new universality class of Euclidean first-passage percolation, where local orientational memory reshapes transport properties and challenges existing bounds for random spatial networks.

cond-mat.dis-nn↗

arXiv2025

Universal roughness and the dynamics of urban expansion

Urban sprawl reshapes cities, yet its quantitative laws remain elusive. Analyzing built-up expansion in 19 cities (1985-2015) with tools from surface growth physics in radial geometry, we reveal anisotropic, branch-like growth and a piecewise linear scaling between area and population. We uncover a robust local roughness exponent $α_{\text{loc}}\approx 0.54$, coexisting with variable $β$ and $z$. This unusual coexistence of universal and variable exponents offers a rare empirical testbed for nonequilibrium growth and an empirical basis for modeling urban sprawl.

physics.soc-ph↗

arXiv2025

Scale-free Points-of-Interest Distribution in a City Emerging from Homogeneous Poissonian-point Processes

Urban systems often exhibit scale-invariant properties, with power-law distributions observed in various spatial and temporal patterns of human behavior. A prominent example is the distribution of commercial activities and other Points of Interest (POIs) across cities. However, the mechanisms by which such heavy-tailed behaviors emerge from local urban dynamics remain poorly understood. In this work, we demonstrate that global inhomogeneity in the spatial distribution of POIs can arise from the aggregation of locally homogeneous processes. Using Foursquare data from the city of Bologna, we show that POI distributions exhibit clear power-law scaling when analyzed at city scale. We develop a theoretical framework in which this behavior naturally emerges from spatial clusters defined by shared intensity levels across disjoint areas, rather than spatial contiguity. By analytically and empirically linking these local processes to the observed global distribution, we provide a generative explanation for the emergence of scale-free patterns in urban commercial structure. To further relax the assumptions underlying the purely spatial model, and to account for the empirical observation that areas with similar activity intensity can be spatially disjoint, we introduce a hybrid hierarchical approach that combines spatial clustering with statistical heterogeneity across regions of comparable density, modeled via Poisson mixtures. This enables us to capture real-world deviations from local regularity while preserving interpretability. Our findings highlight a key insight: complex global phenomena in cities can arise from the spatial superposition of simple, locally uniform dynamics. This connection between micro-level homogeneity and macro-scale complexity offers new tools for interpreting, modeling, and classifying urban space.

physics.soc-ph↗