arXiv subjects

Seonwoo Kim

Publications and source records attributed to Seonwoo Kim.

At least 19 recordsLinked to original sources

arXiv2026

Condensation and metastability in the supercritical two-species zero-range process via resolvent and $H^1$-approximation

In this article, we investigate the two-species zero-range process, a multi-species generalization of the classical zero-range process. First, we analyze its condensation regime, which directly parallels its single-species counterpart. As our main result, we establish the dynamical metastable behavior of the location of the single condensate, showing that its motion is governed by a simple Markov chain on the accelerated time scale $N^{1+\alpha}$, where $N$ denotes the total number of particles in the system and the parameter $\alpha>1$ governs the attractivity of the system. Another novelty of this work lies in the proof technique, which integrates the recently developed resolvent approach with the $H^{1}$-approximation method to rigorously characterize metastability.

math.PR↗

arXiv2026

Metastability of interacting stochastic systems with countably many metastable states: beyond positive recurrence

Metastability is typically formulated for systems with finitely many metastable states, most often in positively recurrent settings. In this article, we extend the resolvent framework for metastability to Markov processes with countably many metastable states, thereby encompassing null-recurrent and transient dynamics. For a family of processes on locally compact Polish spaces, we prove, under a mild boundary regularity assumption, that the asymptotic flatness of microscopic resolvent solutions, supplemented by two compactness conditions, is equivalent to convergence in law of the projected trace processes to a limiting Markov chain and to the negligibility of the time spent outside the metastable sets. We apply this framework to two non-compact stochastic systems. First, we study a condensing inclusion process on a countably infinite, uniformly locally finite graph, in a setting where the process may be null recurrent or transient. We prove that the condensate location converges to a weighted random walk on the underlying graph, while the time spent away from the fully condensed configurations is negligible. Second, we study a small-noise one-dimensional Langevin diffusion with countably many stable equilibria, without assuming ergodicity. In the Eyring-Kramers time scale associated with the minimal energy barrier, we establish local equilibration inside each well, convergence of the well-index process to an explicit nearest-neighbor Markov chain on $\mathbb Z$, and negligibility of inter-well excursions. Together, these results broaden the scope of resolvent-based metastability theory beyond finite metastable state spaces and positive recurrence.

math.PR↗

arXiv2026

Sharp freezing time estimates for the subcritical Facilitated Exclusion Process

We investigate the exact transience time of the Facilitated Exclusion Process (FEP) on the one-dimensional torus with $N$ sites. The FEP exhibits an active/inactive phase transition at critical density $1/2$, such that in the subcritical density regime $(0,1/2)$, it becomes frozen after a finite time period -- the transience time or freezing time. We first show that for the FEP starting from a Bernoulli product measure of marginal density $\rho \in (0,1/2)$, the transience time has exactly the scale of $\Theta(\log^3 N)$. Secondly, we prove that in the near-critical case $\rho \simeq 1/2 - N^{-\alpha}$ for $\alpha \in (0,1)$, the transience time is polynomial and has a scale of $N^{1 \wedge (2\alpha)}$. The key idea is to estimate the typical size of locally supercritical intervals of the initial distribution, which has order $\log N$ in the subcritical case and $N^{1 \wedge (2\alpha)}$ in the near-critical case. In the subcritical case this is enough, whereas in the near-critical case we need additional dynamical decorrelation inequalities to apply this static result to estimate the freezing time.

math.PR↗

arXiv2026

Schema-Agnostic Knowledge Graph Construction via Hybrid Ontology Discovery for Cyber Threat Intelligence

Cyber threat intelligence (CTI) reports now serve as essential resources for capturing adversary tactics, techniques, and procedures observed in modern attack campaigns. While traditional CTI platforms reduce this intelligence to isolated indicators through fixed schemas such as STIX, ontology-based representations preserve the semantic relationships needed for structured threat analysis. However, existing approaches for ontology-aligned CTI extraction face three challenges: (i) schema-specific pipelines that require manual reconfiguration whenever the schema changes, (ii) prompt-based schema inclusion that fails to scale on large ontologies such as UCO, and (iii) reliance on enterprise LLM APIs that conflicts with privacy constraints when integrating sensitive internal incident data. In this paper, we present ANCHOR, a schema-agnostic CTI knowledge graph construction system that bridges LLMs and formal ontology schemas. At the core of ANCHOR is hybrid ontology discovery, a search-and-navigate mechanism that dynamically explores large-scale ontology schemas, combined with SHACL-based validation to enforce schema-compliant type assignments. Experimental results on the UCO, STIX, and MALOnt schemas show that ANCHOR outperforms existing baselines in ontology typing and schema compliance. In addition, ANCHOR with a local LLM closely matches enterprise LLM typing performance, enabling privacy-preserving CTI analysis with high fidelity.

cs.CR↗

arXiv2026

Convergence of the Condensing Symmetric Inclusion Process on the Torus in the Thermodynamical Limit to Coalescing Brownian Motions

We investigate the saturation regime of the condensing symmetric inclusion process on the discrete one-dimensional torus in the thermodynamical limit. In this regime, the total mass concentrates on a finite number of sites, forming condensates. Our main result establishes that, under appropriate scaling, the positions of the condensates converge to a system of coalescing Brownian motions on the continuum torus. In particular, condensates perform diffusive motion until they meet, at which point they merge and their masses coagulate. This provides a rigorous derivation of a macroscopic coalescing diffusion from an underlying interacting particle system with condensation. The main technical difficulty arises from the complicated coalescence mechanism of two condensates of particles, whose trajectories are very difficult to track completely. The key idea is to control the coalescing time instead and prove that it is negligible compared to the time-scale of condensate movement. By combining this with precise estimates of movements without coalescence, we can prove its convergence to coalescing Brownian motions.

math.PR↗

arXiv2026

Sharp mixing time asymptotics of Glauber dynamics for the Curie-Weiss-Potts model at low temperatures

In this article, we derive a sharp mixing time estimate of the Glauber dynamics for the Curie-Weiss-Potts model in the low-temperature regime. In contrast to the high-temperature regime studied by Cuff et al. (J. Stat. Phys. 149: 432-477, 2012), in which the Gibbs measure is concentrated around the equiproportional distribution of spins, the Gibbs measure in the low-temperature regime is concentrated on multiple states, each with a dominant number of a single spin. Consequently, global mixing of the system requires sufficiently many transitions between these states. Since these transitions are well explained by the phenomenon of metastability, the theory of metastability plays a central role in the analysis of slow mixing. In particular, the sharp asymptotics for the mixing time is given by the mixing time of the limit Markov chain, which describes the metastable behavior of the dynamics, multiplied by the metastable transition time-scale. As a byproduct, we verify that it does not exhibit a cutoff phenomenon.

math.PR↗

arXiv2025

K-DRIFT: Unveiling New Imagery of the Hidden Universe

Low-surface-brightness (LSB) structures play a crucial role in understanding galaxy evolution by providing significant insights into galaxy interactions, the histories of mass assembly, and the distribution of dark matter. Nevertheless, their inherently faint nature, coupled with observational difficulties such as stray light interference and variations in the sky background, has significantly impeded comprehensive studies of LSB features. The KASI Deep Rolling Imaging Fast Telescope (K-DRIFT) project aims to address these observational challenges by developing off-axis freeform three-mirror telescopes and observational strategies specifically designed for LSB imaging surveys. The first generation of the K-DRIFT (K-DRIFT G1) has been successfully completed, and the forthcoming survey, scheduled to commence shortly, is expected to yield novel insights into the LSB universe. This paper outlines the scientific motivations of the project, discusses the technical challenges encountered, highlights the innovative solutions devised, and describes the future trajectory of the K-DRIFT.

astro-ph.GA↗

arXiv2025

A large thermal energy reservoir in the nascent intracluster medium at a redshift of 4.3

Most baryons in present-day galaxy clusters exist as hot gas ($\boldsymbol{\gtrsim10^7\,\rm}\mathrm{K}$), forming the intracluster medium (ICM). Cosmological simulations predict that the mass and temperature of the ICM rapidly decrease with increasing cosmological redshift, as intracluster gas in younger clusters is still accumulating and being heated. The thermal Sunyaev-Zeldovich (tSZ) effect arises when cosmic microwave background (CMB) photons are scattered to higher energies through interactions with energetic electrons in hot ICM, leaving a localized decrement in the CMB at a long wavelength. The depth of this decrement is a measure of the thermal energy and pressure of the gas. To date, the effect has been detected in only three systems at or above $z\sim2$, when the Universe was 4 billion years old, making the time and mechanism of ICM assembly uncertain. Here, we report observations of this effect in the protocluster SPT2349$-$56 with Atacama Large Millimeter/submillimeter Array (ALMA). SPT2349$-$56 contains a large molecular gas reservoir, with at least 30 dusty star-forming galaxies (DSFGs) and three radio-loud active galactic nuclei (AGN) in a 100-kpc region at $z=4.3$, corresponding to 1.4 billion years after the Big Bang. The observed tSZ signal implies a thermal energy of $\mathbf{\sim 10^{61}\,\mathrm{erg}}$, exceeding the possible energy of a virialized ICM by an order of magnitude. Contrary to current theoretical expectations, the strong tSZ decrement in SPT2349$-$56 demonstrates that substantial heating can occur and deposit a large amount of thermal energy within growing galaxy clusters, overheating the nascent ICM in unrelaxed structures, two billion years before the first mature clusters emerged at $\mathbf{z \sim 2}$.

astro-ph.GA↗

arXiv2025

Spectral gap of the KMP and other stochastic exchange models on arbitrary graphs

We present a simple strategy to derive universal bounds on the spectral gap of reversible stochastic exchange models on arbitrary graphs. The Kipnis-Marchioro-Presutti (KMP) model, the harmonic process (HP), and the immediate exchange model (IEM) are all examples that fall into this class. Our upper and lower bounds depend only on two features: worst-case linear statistics and a kinetic factor, which is, in essence, graph-independent. For the three aforementioned examples, these bounds are sharp, and even saturate to an identity for HP and IEM in some log-concave regimes. The proof -- which yields bounds for eigenvalues even in the non-reversible context -- crucially exploits the rigidity of the eigenstructure of these models and quantitative contraction rates of the corresponding hidden parameter models recently introduced in [DMFG24, GRT25].

math.PR↗

arXiv2025

Metastable Hierarchy in Abstract Low-Temperature Lattice Models

In this article, we review the metastable hierarchy in low-temperature lattice models. In the first part, we state that for any abstract lattice system governed by a Hamiltonian potential and evolving according to a Metropolis-type dynamics, there exists a hierarchical decomposition of the collection of stable plateaux in the system into multiple $\mathfrak{m}$ levels, such that at each level there exist tunneling metastable transitions between the stable plateaux, which can be characterized by convergence to a simple Markov chain as the inverse temperature $β$ tends to infinity. In the second part, we collect several examples that realize this hierarchical structure of metastability. In order to fix the ideas, we select the Ising model as our lattice system and discuss its metastable behavior under four different types of dynamics, namely the Glauber dynamics with positive/zero external fields and the Kawasaki dynamics with few/many particles. This review article is submitted to the proceedings of the event PSPDE XII, held at the University of Trieste from September 9-13, 2024.

math.PR↗

arXiv2025

$Γ$-expansion of the measure-current large deviations rate functional of non-reversible finite-state Markov chains

Consider a sequence of continuous-time Markov chains $(X^{(n)}_t:t\ge 0)$ evolving on a fixed finite state space $V$. Let $I_n$ be the measure-current large deviations rate functional for $X^{(n)}_t$, as $t\to\infty$. Under a hypothesis on the jump rates, we prove that $I_n$ can be written as $I_n = \mathbf I^{(0)} \,+\, \sum_{1\le p\le \mathfrak q} (1/θ^{(p)}_n) \, \mathbf I^{(p)}$ for some rate functionals $\mathbf I^{(p)}$. The weights $θ^{(p)}_n$ correspond to the time-scales at which the sequence of Markov chains $X^{(n)}_t$ evolves among the metastable wells, and the rate functionals $\mathbf I^{(p)}$ characterise the asymptotic Markovian dynamics among these wells. This expansion provides therefore an alternative description of the metastable behavior of a sequence of Markovian dynamics. Together with the results in \cite{bgl-24,l-gamma}, this work finishes the project of characterising the hierarchical metastable behavior of finite-state Markov chains by means of the $Γ$-expansion of large deviations rate functionals. In addition, we present optimal conditions under which the measure (Donsker-Varadhan) or the measure-current large deviations rate functional determines the original dynamics, and calculate the first and second derivatives of the measure large deviations rate functional, thereby generalising the results for i.i.d. random variables.

math.PR↗

arXiv2024

One- and two-particle spectral gap identities for the symmetric inclusion process and related models

The symmetric inclusion process (SIP) models particles diffusing on a graph with mutual attraction. We recently showed that, in the log-concave regime (where diffusivity dominates interaction), the spectral gap of the conservative SIP matches that of a single particle. In this paper, our main result demonstrates that this identity generally fails outside this regime, but always holds for the non-conservative SIP, regardless of the interaction strength. When this one-particle spectral gap identity breaks down, we derive sharp bounds for the gap in terms of diffusivity, and reveal a two-particle spectral gap identity in the vanishing diffusivity limit. Our approach leverages the rigid eigenstructure of SIP, refined comparisons of Dirichlet forms for arbitrary diffusivity and particle numbers, and techniques from slow-fast system analysis. These findings extend to the dual interacting diffusion known as Brownian energy process, and shed some light on the spectral gap behavior for related Dirichlet-reversible systems on general, non-mean-field, geometries.

math.PR↗

arXiv2024

Metastable hierarchy in abstract low-temperature lattice models: an application to Kawasaki dynamics for Ising lattice gas with macroscopic number of particles

This article is divided into two parts. In the first part, we study the hierarchical phenomenon of metastability in low-temperature lattice models in the most general setting. Given an abstract dynamical system governed by a Hamiltonian function, we prove that there exists a hierarchical decomposition of the collection of stable plateaux in the system into multiple $\mathfrak{m}$ levels, such that at each level there exist tunneling metastable transitions between the stable plateaux, which can be characterized by convergence to an explicit simple Markov chain as the inverse temperature $β$ tends to infinity. In the second part, as an application, we characterize the $3$-level metastable hierarchy in Kawasaki dynamics for Ising lattice gas with macroscopic number of particles. We prove that the ground states in this model are those in which the particles line up and form a one-dimensional strip, and identify the full structure relevant to the tunneling transitions between these ground states. In particular, the results differ from the previous work [5] in that the particles in the ground states are likely to form a strip rather than a square droplet. The main tool is the resolvent approach to metastability, recently developed in [24]. Along with the analysis, we present a theorem on the sharp asymptotics of the exit distribution from cycles, which to the author's knowledge is not known in the community and therefore may be of independent interest.

math.PR↗

arXiv2023

TEMPLATES: A Robust Outlier Rejection Method for JWST/NIRSpec Integral Field Spectroscopy

We describe a custom outlier rejection algorithm for JWST/NIRSpec integral field spectroscopy. This method uses a layered sigma clipping approach that adapts clipping thresholds based upon the spatial profile of the science target. We find that this algorithm produces a robust outlier rejection while simultaneously preserving the signal of the science target. Originally developed as a response to unsatisfactory initial performance of the jwst pipeline outlier detection step, this method works either as a standalone solution, or as a supplement to the current pipeline software. Comparing leftover (i.e., not flagged) artifacts with the current pipeline's outlier detection step, we find that our method results in one fifth as many residual artifacts as the jwst pipeline. However, we find a combination of both methods removes nearly all artifacts -- an approach that takes advantage of both our algorithm's robust outlier rejection and the pipeline's use of individual dithers. This combined approach is what the TEMPLATES Early Release Science team has converged upon for our NIRSpec observations. Finally, we publicly release the code and Jupyter notebooks for the custom outlier rejection algorithm.

astro-ph.IM↗

arXiv2023

JWST Early Release Science Program TEMPLATES: Targeting Extremely Magnified Panchromatic Lensed Arcs and their Extended Star formation

This paper gives an overview of TEMPLATES, a JWST Early Release Science program that targeted four extremely bright, gravitationally lensed galaxies: two extremely dusty, two with low attenuation, as templates for galaxy evolution studies with JWST. TEMPLATES obtains a common set of spectral diagnostics for these 1.3 < z < 4.2 galaxies, in particular H alpha, Paschen alpha, and the rest-frame optical and near-infrared continua. In addition, two of the four targets have JWST coverage of [O III] 5007 Angstrom and H beta; the other two targets have have JWST coverage of PAH 3.3 micron and complementary ALMA data covering the [C II] 158 micron emission line. The science goals of TEMPLATES are to demonstrate attenuation-robust diagnostics of star formation, map the distribution of star formation, compare the young and old stellar populations, and measure the physical conditions of star formation and their spatial variation across the galaxies. In addition, TEMPLATES has technical goals to establish best practices for the Integral Field Units (IFU) within the NIRSpec and MIRI instruments, both in terms of observing strategy and in terms of data reduction. The paper describes TEMPLATES's observing program, scientific and technical goals, data reduction methods, and deliverables, including high-level data products and data reduction cookbooks.

astro-ph.GA↗

arXiv2023

Hierarchical structure of metastability in the reversible inclusion process: third time scale and complete characterization

In this article, we study the hierarchical structure of metastability in the reversible inclusion process. We fully characterize the third time scale of metastability subject to any underlying geometry of the system and prove that this is the last time scale. We also demonstrate that there are no other meaningful time scales except the three identified ones. This work completes the verification of the conjecture made in [7] which was partially resolved on the first time scale in [7] and on the second time scale in [25]. Main tools are potential-theoretic approach and martingale approach to metastability; we thoroughly investigate the highly-complicated energy landscape of the system to construct suitable test objects to provide sharp asymptotics on capacities.

math.PR↗

arXiv2023

Second Time Scale of the Metastability of Reversible Inclusion Processes

We investigate the second time scale of the metastable behavior of the reversible inclusion process in an extension of the study by [Bianchi, Dommers, and Giardinà, Electronic Journal of Probability, 22: 1-34, 2017], which presented the first time scale of the same model and conjectured the scheme of multiple time scales. We show that $N/d_{N}^{2}$ is indeed the correct second time scale for the most general class of reversible inclusion processes, and thus prove the first conjecture of the foresaid study. Here, $N$ denotes the number of particles, and $d_{N}$ denotes the small scale of randomness of the system. The main obstacles of this research arise in calculating the sharp asymptotics for the capacities, and in the fact that the methods employed in the former study are not directly applicable due to the complex geometry of particle configurations. To overcome these problems, we first thoroughly examine the landscape of the transition rates to obtain a proper test function of the equilibrium potential, which provides the upper bound for the capacities. Then, we modify the induced test flow and precisely estimate the equilibrium potential near the metastable valleys to obtain the correct lower bound for the capacities.

math.PR↗

arXiv2023

Spatial variations in aromatic hydrocarbon emission in a dust-rich galaxy

Dust grains absorb half of the radiation emitted by stars throughout the history of the universe, re-emitting this energy at infrared wavelengths. Polycyclic aromatic hydrocarbons (PAHs) are large organic molecules that trace millimeter-size dust grains and regulate the cooling of the interstellar gas within galaxies. Observations of PAH features in very distant galaxies have been difficult due to the limited sensitivity and wavelength coverage of previous infrared telescopes. Here we present JWST observations that detect the 3.3um PAH feature in a galaxy observed less than 1.5 billion years after the Big Bang. The high equivalent width of the PAH feature indicates that star formation, rather than black hole accretion, dominates the infrared emission throughout the galaxy. The light from PAH molecules, large dust grains, and stars and hot dust are spatially distinct from one another, leading to order-of-magnitude variations in the PAH equivalent width and the ratio of PAH to total infrared luminosity across the galaxy. The spatial variations we observe suggest either a physical offset between the PAHs and large dust grains or wide variations in the local ultraviolet radiation field. Our observations demonstrate that differences in the emission from PAH molecules and large dust grains are a complex result of localized processes within early galaxies.

astro-ph.GA↗