arXiv subjects

Aser Cortines

Publications and source records attributed to Aser Cortines.

At least 19 recordsLinked to original sources

arXiv2026

Aging in a spin glass with logarithmic correlations

We consider a continuous-time random walk on the discrete two dimensional box, driven by the discrete Gaussian Free Field (DGFF) acting as potential: When at a vertex, the walk waits an exponentially distributed time with mean given by the exponential of the field times an inverse temperature parameter and then jumps to one of its neighbors uniformly at random. We prove that when the temperature is below the critical value the walk exhibits ``aging'' at a range of pre-equilibrium time scales: Observed at any such time and then again after an additional time of the same order, there is a positive probability that the walk is found within finite distance from where it was before, with this probability given asymptotically by the Generalized Arcsine Law with a temperature-dependent parameter. We show that this is a consequence of an intricate trapping mechanism which localizes the walk for periods of time which increase with the age of the system, and describe the complex structure of the underlying trapping landscape, which is intimately related to the geometry of the near-extreme level-sets of the DGFF. Altogether, this work demonstrates for the first time an Arcsine-Law aging in the case of a spin-glass-type system with a logarithmically correlated potential, throughout its glassy phase, as predicted in the physic literature.

math.PR↗

arXiv2026

STN-GPR: A Singularity Tensor Network Framework for Efficient Option Pricing

We develop a tensor-network surrogate for option pricing, targeting large-scale portfolio revaluation problems arising in market risk management (e.g., VaR and Expected Shortfall computations). The method involves representing high-dimensional price surfaces in tensor-train (TT) form using TT-cross approximation, constructing the surrogate directly from black-box price evaluations without materializing the full training tensor. For inference, we use a Laplacian kernel and derive TT representations of the kernel matrix and its closed-form inverse in the noise-free setting, enabling TT-based Gaussian process regression without dense matrix factorization or iterative linear solves. We found that hyperparameter optimization consistently favors a large kernel length-scale and show that in this regime the GPR predictor reduces to multilinear interpolation for off-grid inputs; we also derive a low-rank TT representation for this limit. We evaluate the approach on five-asset basket options over an eight dimensional parameter space (asset spot levels, strike, interest rate, and time to maturity). For European geometric basket puts, the tensor surrogate achieves lower test error at shorter training times than standard GPR by scaling to substantially larger effective training sets. For American arithmetic basket puts trained on LSMC data, the surrogate exhibits more favorable scaling with training-set size while providing millisecond-level evaluation per query, with overall runtime dominated by data generation.

q-fin.PR↗

arXiv2025

Quantum-based QoE Optimization in Advanced Cellular Networks: Integration and Cloud Gaming Use Case

This work explores the integration of Quantum Machine Learning (QML) and Quantum-Inspired (QI) techniques for optimizing end-to-end (E2E) network services in telecommunication systems, particularly focusing on 5G networks and beyond. The application of QML and QI algorithms is investigated, comparing their performance with classical Machine Learning (ML) approaches. The present study employs a hybrid framework combining quantum and classical computing leveraging the strengths of QML and QI, without the penalty of quantum hardware availability. This is particularized for the optimization of the Quality of Experience (QoE) over cellular networks. The framework comprises an estimator for obtaining the expected QoE based on user metrics, service settings, and cell configuration, and an optimizer that uses the estimation to choose the best cell and service configuration. Although the approach is applicable to any QoE-based network management, its implementation is particularized for the optimization of network configurations for Cloud Gaming services. Then, it is evaluated via performance metrics such as accuracy and model loading and inference times for the estimator, and time to solution and solution score for the optimizer. The results indicate that QML models achieve similar or superior accuracy to classical ML models for estimation, while decreasing inference and loading times. Furthermore, potential for better performance is observed for higher-dimensional data, highlighting promising results for higher complexity problems. Thus, the results demonstrate the promising potential of QML in advancing network optimization, although challenges related to data availability and integration complexities between quantum and classical ML are identified as future research lines.

cs.NI↗

arXiv2025

Lightweight Cloud Masking Models for On-Board Inference in Hyperspectral Imaging

Cloud and cloud shadow masking is a crucial preprocessing step in hyperspectral satellite imaging, enabling the extraction of high-quality, analysis-ready data. This study evaluates various machine learning approaches, including gradient boosting methods such as XGBoost and LightGBM as well as convolutional neural networks (CNNs). All boosting and CNN models achieved accuracies exceeding 93%. Among the investigated models, the CNN with feature reduction emerged as the most efficient, offering a balance of high accuracy, low storage requirements, and rapid inference times on both CPUs and GPUs. Variations of this version, with only up to 597 trainable parameters, demonstrated the best trade-off in terms of deployment feasibility, accuracy, and computational efficiency. These results demonstrate the potential of lightweight artificial intelligence (AI) models for real-time hyperspectral image processing, supporting the development of on-board satellite AI systems for space-based applications.

cs.CV↗

arXiv2025

Quantum-Inspired Solver for Simulating Material Deformations

This paper explores the application of tensor networks (TNs) to the simulation of material deformations within the framework of linear elasticity. Material simulations are essential computational tools extensively used in both academic research and industrial applications. TNs, originally developed in quantum mechanics, have recently shown promise in solving partial differential equations (PDEs) due to their potential for exponential speedups over classical algorithms. Our study successfully employs TNs to solve linear elasticity equations with billions of degrees of freedom, achieving exponential reductions in both memory usage and computational time. These results demonstrate the practical viability of TNs as a powerful classical backend for executing quantum-inspired algorithms with significant efficiency gains. This work is based on our research conducted with IKERLAN.

quant-ph↗

arXiv2024

Encoding of Probability Distributions for Quantum Monte Carlo Using Tensor Networks

The application of Tensor Networks (TN) in quantum computing has shown promise, particularly for data loading. However, the assumption that data is readily available often renders the integration of TN techniques into Quantum Monte Carlo (QMC) inefficient, as complete probability distributions would have to be calculated classically. In this paper the tensor-train cross approximation (TT-cross) algorithm is evaluated as a means to address the probability loading problem. We demonstrate the effectiveness of this method on financial distributions, showcasing the TT-cross approach's scalability and accuracy. Our results indicate that the TT-cross method significantly improves circuit depth scalability compared to traditional methods, offering a more efficient pathway for implementing QMC on near-term quantum hardware. The approach also shows high accuracy and scalability in handling high-dimensional financial data, making it a promising solution for quantum finance applications.

quant-ph↗

arXiv2024

Wetting Transition on Trees I: Percolation With Clustering

A new ``Percolation with Clustering'' (PWC) model is introduced, where (the probabilities of) site percolation configurations on the leaf set of a binary tree are rewarded exponentially according to a generic function, which measures the degree of clustering in the configuration. Conditions on such ``clustering function'' are given for the existence of a limiting free energy and a wetting transition, namely the existence of a non-trivial percolation parameter threshold above and only above which the set of ``dry'' (open) sites have an asymptotic density. Several examples of clustering functions are given and studied using the general theory. The results here will be used in a sequel paper to study the wetting transition for the discrete Gaussian free field on the tree subject to a hard wall constraint.

math.PR↗

arXiv2020

A simple backward construction of Branching Brownian motion with large displacement and applications

In this article, we study the extremal processes of branching Brownian motions conditioned on having an unusually large maximum. The limiting point measures form a one-parameter family and are the decoration point measures in the extremal processes of several branching processes, including branching Brownian motions with variable speed and multitype branching Brownian motions. We give a new, alternative representation of these point measures and we show that they form a continuous family. This also yields a simple probabilistic expression for the constant that appears in the large deviation probability of having a large displacement. As an application, we show that Bovier and Hartung (2015)'s results about variable speed branching Brownian motion also describe the extremal point process of branching Ornstein-Uhlenbeck processes.

math.PR↗

arXiv2019

The Structure of Extreme Level Sets in Branching Brownian Motion

We study the structure of extreme level sets of a standard one dimensional branching Brownian motion, namely the sets of particles whose height is within a fixed distance from the order of the global maximum. It is well known that such particles congregate at large times in clusters of order-one genealogical diameter around local maxima which form a Cox process in the limit. We add to these results by finding the asymptotic size of extreme level sets and the typical height and shape of those clusters which carry such level sets. We also find the right tail decay of the distribution of the distance between the two highest particles. These results confirm two conjectures of Brunet and Derrida, 2011. The proofs rely on studying the cluster distribution and should carry over to the branching random walk and the two-dimensional discrete Gaussian free field with no conceptual difficulty.

math.PR↗

arXiv2019

More on the Structure of Extreme Level Sets in Branching Brownian Motion

This work is a continuation of the manuscript "the structure of extreme level sets in branching Brownian motion", in which the same authors studied the fine structure of the extreme level sets of branching Brownian motion, namely the sets of particles whose height is within a finite distance from the global maximum. It is well known that such particles congregate at large times in clusters of order-one genealogical diameter around local maxima which form a Cox process in the limit. Our main finding here is that most of the particles in an extreme level set come from only a small fraction of the clusters, which are atypically large.

math.PR↗

arXiv2019

Decorated Random Walk Restricted to Stay Below a Curve (Supplement Material)

We consider a one dimensional random-walk-like process, whose steps are centered Gaussians with variances which are determined according to the sequence of arrivals of a Poisson process on the line. This process is decorated by independent random variables which are added at each step, but do not get accumulated. We study the probability that such process, conditioned to form a bridge, stays below a curve which grows at most polynomially fast away from the boundaries, with exponent less than one half. Both bounds and asymptotics are derived. These estimates are used in the manuscript "the structure of extreme level sets in branching Brownian motion" by the same authors, to which this manuscript is a supplement.

math.PR↗

arXiv2019

A Scaling Limit for the Cover Time of the Binary Tree

We consider a continuous time random walk on the rooted binary tree of depth $n$ with all transition rates equal to one and study its cover time, namely the time until all vertices of the tree have been visited. We prove that, normalized by $2^{n+1} n$ and then centered by $(\log 2) n - \log n$, the cover time admits a weak limit as the depth of the tree tends to infinity. The limiting distribution is identified as that of a Gumbel random variable with rate one, shifted randomly by the logarithm of the sum of the limits of the derivative martingales associated with two negatively correlated discrete Gaussian free fields on the infinite version of the tree. The existence of the limit and its overall form were conjectured in the literature. Our approach is quite different from those taken in earlier works on this subject and relies in great part on a comparison with the extremal landscape of the discrete Gaussian free field on the tree.

math.PR↗

arXiv2018

Dynamical Freezing in a Spin Glass System with Logarithmic Correlations

We consider a continuous time random walk on the two-dimensional discrete torus, whose motion is governed by the discrete Gaussian free field on the corresponding box acting as a potential. More precisely, at any vertex the walk waits an exponentially distributed time with mean given by the exponential of the field and then jumps to one of its neighbors, chosen uniformly at random. We prove that throughout the low-temperature regime and at in-equilibrium timescales, the process admits a scaling limit as a spatial K-process driven by a random trapping landscape, which is explicitly related to the limiting extremal process of the field. Alternatively, the limiting process is a supercritical Liouville Brownian motion with respect to the continuum Gaussian free field on the box. This demonstrates rigorously and for the first time, as far as we know, a dynamical freezing in a spin glass system with logarithmically correlated energy levels.

math.PR↗

arXiv2018

Branching-stable point measures and processes

We introduce and study the class of branching-stable point measures, which can be seen as an analog of stable random variables when the branching mechanism for point measures replaces the usual addition. In contrast with the classical theory of stable (Lévy) processes, there exists a rich family of branching-stable point measures with \emph{negative} scaling exponent, which can be described as certain Crump-Mode-Jagers branching processes. We investigate the asymptotic behavior of their cumulative distribution functions, that is, the number of atoms in $(-\infty, x]$ as $x\to \infty$, and further depict the genealogical lineage of typical atoms. For both results, we rely crucially on the work of Biggins.

math.PR↗

arXiv2018

The genealogy of an exactly solvable Ornstein-Uhlenbeck type branching process with selection

We study the genealogy of a solvable population model with $N$ particles on the real line which evolves according to a discrete-time branching process with selection. At each time step, every particle gives birth to children around $a$ times its current position, where $a>0$ is a parameter of the model. Then, the $N$ rightmost new-born children are selected to form the next generation. We show that the genealogical trees of the process converge to those of a Beta coalescent as $N \to \infty$. The process we consider can be seen as a toy-model version of a continuous-time branching process with selection, in which particles move according to independent Ornstein-Uhlenbeck processes. The parameter $a$ is akin to the pulling strength of the Ornstein-Uhlenbeck motion.

math.PR↗

arXiv2016

A $N$-branching random walk with random selection

We consider an exactly solvable model of branching random walk with random selection, which describes the evolution of a population with $N$ individuals on the real line. At each time step, every individual reproduces independently, and its offspring are positioned around its current locations. Among all children, $N$ individuals are sampled at random without replacement to form the next generation, such that an individual at position $x$ is chosen with probability proportional to $\mathrm{e}^{βx}$. We compute the asymptotic speed and the genealogical behavior of the system.

math.PR↗

arXiv2016

The genealogy of a solvable population model under selection with dynamics related to directed polymers

We consider a stochastic model describing a constant size $N$ population that may be seen as a directed polymer in random medium with $N$ sites in the transverse direction. The population dynamics is governed by a noisy traveling wave equation describing the evolution of the individual fitnesses. We show that under suitable conditions the generations are independent and the model is characterized by an extended Wright-Fisher model, in which the individual $i$ has a random fitness $η_i$ and the joint distribution of offspring $(ν_1,\ldots,ν_N)$ is given by a multinomial law with $N$ trials and probability outcomes $η_i$'s. We then show that the average coalescence times scales like $\log N$ and that the limit genealogical trees are governed by the Bolthausen-Sznitman coalescent, which validates the predictions by Brunet, Derrida, Mueller and Munier for this class of models. We also study the extended Wright-Fisher model, and show that, under certain conditions on $η_i$, the limit may be Kingman's coalescent, a coalescent with multiple collisions, or a coalescent with simultaneous multiple collisions.

math.PR↗

arXiv2015

Finite-size corrections to the speed of a branching-selection process

We consider a particle system studied by E. Brunet and B. Derrida, which evolves according to a branching mechanism with selection of the fittest keeping the population size fixed and equal to $N$. The particles remain grouped and move like a travelling front driven by a random noise with a deterministic speed. Because of its mean-field structure, the model can be further analysed as $N \to \infty$. We focus on the case where the noise lies in the max-domain of attraction of the Weibull extreme value distribution and show that under mild conditions the correction to the speed has universal features depending on the tail probabilities.

math.PR↗