Organized 01

## Coulomb Gases (Organizer: Paul Jung)

Conference
9:30 PM — 10:00 PM KST
Local
Jul 19 Mon, 8:30 AM — 9:00 AM EDT

### Outliers for Coulomb gases

8
We will be interested in a two-dimensional model of n positively charged particles at equilibrium. Our systems will be attracted to a background with negative charge distribution, and it will be seen that, as n goes to infinity and in the regions where there is no background charge, an interesting phenomenon occurs.

It is based on a joint work with Raphael Butez, Alon Nishry and Aron Wennman (arXiv:1811.12225 and arXiv:2104.03959).

### Edge behaviors of 2D Coulomb gases with boundary confinements

Seong-Mi Seo (Korea Institute for Advanced Study)

10
In this talk, we will consider the local statistics of a planar Coulomb gas system which is determinantal. In a suitable external field, the Coulomb particles tend to accumulate on a set called a droplet, which is the support of the equilibrium measure associated with the external field. The most well-known boundary condition for the gas is the “free boundary”, where the particles are admitted to be outside of the droplet. On the other hand, if a boundary confinement is imposed to force the particles to be completely confined to a set, the edge behavior may change. In the presence of a hard-wall constraint to change the equilibrium, the density of the equilibrium measure acquires a singular component at the hard wall and the Coulomb gas system properly rescaled at the hard wall converges to a determinantal point process which appears in the context of truncated unitary matrices. I will present the edge behaviors of the Coulomb gas under the different boundary confinements and explain two approaches using the asymptotics of orthogonal polynomials and the rescaled version of Ward’s equation from the field theory.

### Large deviations in the quantum quasi-1D jellium

Christian Hirsch (University of Groningen)

5
Wigner's jellium is a model for a gas of electrons. The model consists of $N$ unit negatively charged particles lying in a sea of neutralizing homogeneous positive charge spread out according to Lebesgue measure, and interactions are governed by the Coulomb potential. In this work, we consider the quantum jellium on quasi-one-dimensional spaces with Maxwell-Boltzmann statistics. Using the Feynman-Kac representation, we replace particle locations with Brownian bridges. We then adapt the approach of Leblé and Serfaty (2017) to prove a process-level large deviation principle for the empirical fields of the Brownian bridges.

### Lemniscate ensembles with spectral singularities

Sung-Soo Byun (Seoul National University)

11
In this talk, I will discuss a family of determinantal Coulomb gases, which tend to occupy lemniscate type droplets in the large system. For these lemniscate ensembles under the insertion of a point charge, I will present the scaling limits at the singular boundary point, which are expressed in terms of the solution to the Painlevé IV Riemann-Hilbert problem. I will also explain the main ingredients of the proof, which include a version of the Christoffel-Darboux identity and the strong asymptotic behaviour of the associated orthogonal polynomials.

### Q&A for Organized Contributed Session 01

0
This talk does not have an abstract.

###### Session Chair

Paul Jung (Korea Advanced Institute of Science and Technology (KAIST))

Organized 04

## Interacting Particle Systems and Inclusion Process (Organizer: Cristian Giardinà)

Conference
9:30 PM — 10:00 PM KST
Local
Jul 19 Mon, 8:30 AM — 9:00 AM EDT

### Metastability in the reversible inclusion process

Sander Dommers (University of Hull)

8
In the reversible inclusion process with a fixed number of particles on a finite graph each particle at a site x jumps to site y at rate $(d+\eta_y)r(x,y)$, where d is a diffusion parameter, $\eta_y$ is the number of particles on site y and r(x,y) is the jump rate from x to y of an underlying reversible random walk. When the diffusion d tends to 0 as the number of particles tends to infinity, the particles cluster together to form a condensate. It turns out that these condensates only form on the sites where the underlying random walk spends the most time. Once such a condensate is formed the particles stick together and the condensate performs a random walk itself on much longer timescales, which can be seen as metastable (or tunnelling) behaviour. We study the rates at which the condensate jumps and characterize the behavior on the shortest time scale at which jumps occur. This generalizes work by Grosskinsky, Redig and Vafayi who study the symmetric case. Our analysis is based on the martingale approach by Beltrán and Landim.

This is joint work with Alessandra Bianchi and Cristian Giardinà.

### Metastability in the reversible inclusion process II: multiple timescales

8
The inclusion process (IP) is a stochastic lattice gas where particles perform random walks subjected to mutual attraction, thus providing the natural bosonic counterpart of the well-studied exclusion process. Due to the attractive interaction between particles, the IP can exhibit a condensation transition, where a positive fraction of all particles concentrates on a single site. In this talk, following the setting and results presented by S. Dommers, we consider the reversible IP on a finite set S in the limit of total number of particles going to infinity, and focus on the characterization of multiple timescales. Their presence will be related to some properties of the underlying random walk, and in particular to specific connectivity features of the underlying dynamics when restricted to points that maximize the reversible measure. We approach the problem starting from potential theoretic techniques and following some recent related ideas developed in a few papers we will refer to.

Joint work with S. Dommers and C. Giardinà.

### Condensation and metastability of general Inclusion processes

Seonwoo Kim (Seoul National University)

9
In this talk, we present various results regarding the phenomenon of condensation and metastability of inclusion processes on a wide class of underlying graphs. Condensation denotes the phenomenon when a majority of the particles assemble on a single site. It occurs in various interacting particle systems, including the current one, due to the attractive behavior of the particles. In a bigger time scale, because of the small randomness of the system, the formed condensate breaks up and forms another one on a different site. This is a typical example of the metastable behavior, which is quite ubiquitous in numerous stochastic systems. The metastable behavior of the current model is known to exhibit the scheme of multiple time scales; thus, we first explain the reason of presence of such a scheme. Moreover, the fundamental behavior of metastability dramatically differs between the reversible and non-reversible ones. Therefore, the main results are divided into two parts: reversible case and non-reversible case. In the reversible case, the results are known fairly in details. In the context of multiple time scales scenario, the metastable behavior is fully characterized up to the second time scale. We present the known results along with the conjectures for the unsolved regime. In the non-reversible case, a much more complicated scenario emerges even in the first time scale. The main difficulty is that we do not have an explicit formula for the invariant measure. We explain how to overcome this drawback and characterize the condensation and metastability in the first time scale which generalizes the previous results in the reversible case.

### Condensation of SIP particles and sticky Brownian motion

Gioia Carinci (Università di Modena e Reggio Emilia)

6
The symmetric inclusion process (SIP) is a particle system with attractive interaction. We study its behavior in the condensation regime attained for large values of the attraction intensity. Using Mosco convergence of Dirichlet forms, we prove convergence to sticky Brownian motion for the distance of two SIP particles. We use this result to obtain, via duality, an explicit scaling for the variance of the density field in this regime, for the SIP initially started from a homogeneous product measure. This provides relevant new information on the coarsening dynamics of condensing particle systems on the infinite lattice.
Joint works with M. Ayala, C Giardina and F. Redig

### Condensed phase structure in Inclusion processes

Watthanan Jatuviriyapornchai (Mahidol University)

6
We establish a complete picture of condensation in the inclusion process in the thermodynamic limit. The condensed phase structure is derived by a size-biased sampling of occupation numbers. Our results cover the entire scaling regimes of the diffusion parameter, especially an interesting hierarchical structure characterized by the Poisson-Dirichlet distribution. Whereas our results are rigorous, Monte-Carlo simulation and recursive numerics for partition functions are presented to illustrate the main points.

### Q&A for Organized Contributed Session 04

0
This talk does not have an abstract.

###### Session Chair

Cristian Giardinà (University of Modena and Reggio Emilia)

Organized 22

## Recent Progress of Statistical Inference for Economics and Social Science (Organizer: Eun Ryung Lee)

Conference
9:30 PM — 10:00 PM KST
Local
Jul 19 Mon, 8:30 AM — 9:00 AM EDT

### A spline-based modeling approach for time-Indexed multilevel data

Eun Ryung Lee (Sungkyunkwan University)

7
This paper introduces a spline-based multilevel approach for analyzing a time-indexed data collected from an automated platform. The proposed method is computationally efficient and easy to implement, and useful for analyzing data that have hierarchical structure with varying complexity at different levels. An estimation procedure is developed combining Expectation-Maximization algorithm and nonparametric regression approach. The theoretical properties of the proposed methods are derived. The proposed estimator is shown to belong to a well-known linear smoother class. Thus, further statistical inference can be easily adopted from the existing literature on linear smoothers. An R package for the proposed methodology is provided in an open repository. The effectiveness of the approach is illustrated using music concert event data collected in the United States for several years.

### Impulse response analysis for sparse high-dimensional time series

Carsten Trenkler (University of Mannheim)

6
We consider structural impulse response analysis for sparse high-dimensional vector autoregressive (VAR) systems. First, we present a consistent estimation approach in the high-dimensional setting. Second, we suggest a valid inference procedure. Inference is more involved since standard procedures, like the delta-method, do not lead to valid inference in our set-up. Therefore, by using the local projection equations, we first construct a de-sparsified version of regularized estimators of the moving average parameters that are associated with the VAR system. In order to obtain estimators of the structural impulse responses we combine these de-sparsified estimators with a non-regularized estimator of the contemporaneous impact matrix in such a way that that the high-dimension is taken into account. We show that the estimators of the structural impulse responses have a Gaussian limiting distribution. Moreover, we also present a valid bootstrap procedure. Applications of the inference procedure are confidence intervals of the impulse responses as well as tests for forecast error variance decompositions that are often used to construct connectedness measures. Our procedure is illustrated by means of simulations.

### Revealing cluster structures based on mixed sampling frequencies: with an application to the state-level labor markets

Yeonwoo Rho (Michigan Technological University)

3
This paper proposes a new linearized mixed data sampling (MIDAS) model and develops a framework to infer clusters in a panel regression with mixed frequency data. The linearized MIDAS estimation method is more flexible and substantially simpler to implement than competing approaches. We show that the proposed clustering algorithm successfully recovers true membership in the cross-section, both in theory and in simulations, without requiring prior knowledge of the number of clusters. This methodology is applied to a mixed-frequency Okun’s law model for state-level data in the U.S. and uncovers four meaningful clusters based on the dynamic features of state-level labor markets.

### Semiparametric efficient estimators in heteroscedastic error models

Mijeong Kim (Ewha Womans University)

4
In the mean regression context, this study considers several frequently encountered heteroscedastic error models where the regression mean and variance functions are specified up to certain parameters. An important point we note through a series of analyses is that different assumptions on standardized regression errors yield quite different efficiency bounds for the corresponding estimators. Consequently, all aspects of the assumptions need to be specifically taken into account in constructing their corresponding efficient estimators. This study clarifies the relation between the regression error assumptions and their, respectively, efficiency bounds under the general regression framework with heteroscedastic errors. Our simulation results support our findings; we carry out a real data analysis using the proposed methods where the Cobb-Douglas cost model is the regression mean.

### Q&A for Organized Contributed Session 22

0
This talk does not have an abstract.

###### Session Chair

Eun Ryung Lee (Sungkyunkwan University)