Wei‐Kuo Chen
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View article: On the Replica Symmetric Solution in General Diluted Spin Glasses
On the Replica Symmetric Solution in General Diluted Spin Glasses Open
We present a unifying approach to studying the replica symmetric solution in general diluted spin glass models on random ‐uniform hypergraphs with sparsity parameter . Our result shows that there exist two key regimes in which the model ex…
View article: On the Replica Symmetric Solution in General Diluted Spin Glasses
On the Replica Symmetric Solution in General Diluted Spin Glasses Open
We present a unifying approach to studying the replica symmetric solution in general diluted spin glass models on random $p$-uniform hypergraphs with sparsity parameter $α$. Our result shows that there exist two key regimes in which the mo…
View article: Joint parameter estimations for spin glasses
Joint parameter estimations for spin glasses Open
Spin glass models with quadratic-type Hamiltonians are disordered statistical physics systems with competing ferromagnetic and anti-ferromagnetic spin interactions. The corresponding Gibbs measures belong to the exponential family parametr…
View article: Disorder Chaos in Short-Range, Diluted, and Lévy Spin Glasses
Disorder Chaos in Short-Range, Diluted, and Lévy Spin Glasses Open
In a recent breakthrough [arXiv:2301.04112], Chatterjee proved site disorder chaos in the Edwards-Anderson (EA) short-range spin glass model utilizing the Hermite spectral method. In this paper, we demonstrate the further usefulness of thi…
View article: A Gaussian Convexity for Logarithmic Moment Generating Functions with Applications in Spin Glasses
A Gaussian Convexity for Logarithmic Moment Generating Functions with Applications in Spin Glasses Open
For any convex function $F$ of $n$-dimensional Gaussian vector $g$ with $\mathbb{E} e^{λF(g)}<\infty$ for any $λ>0$, we show that $λ^{-1}\ln \mathbb{E} e^{λF(g)}$ is convex in $λ\in\mathbb{R}$. Based on this convexity, we draw three major …
View article: Some Rigorous Results on the Lévy Spin Glass Model
Some Rigorous Results on the Lévy Spin Glass Model Open
We study the Lévy spin glass model, a fully connected model on $N$ vertices with heavy-tailed interactions governed by a power law distribution of order $0<α<2.$ Our investigation is divided into three cases $0<α<1$, $α=1$, and $1<α<2.$ Wh…
View article: Universality of Superconcentration in the Sherrington-Kirkpatrick Model
Universality of Superconcentration in the Sherrington-Kirkpatrick Model Open
We study the universality of superconcentration for the free energy in the Sherrington-Kirkpatrick (SK) model. In arXiv:0907.3381, Chatterjee showed that when the system consists of $N$ spins and Gaussian disorders, the variance of this qu…
View article: On the TAP equations via the cavity approach in the generic mixed $p$-spin models
On the TAP equations via the cavity approach in the generic mixed $p$-spin models Open
In 1977, Thouless, Anderson, and Palmer (TAP) derived a system of consistent equations in terms of the effective magnetization in order to study the free energy in the Sherrington-Kirkpatrick (SK) spin glass model. The solutions to their e…
View article: Free energy of a diluted spin glass model with quadratic Hamiltonian
Free energy of a diluted spin glass model with quadratic Hamiltonian Open
We study a diluted mean-field spin glass model with a quadratic Hamiltonian. Our main result establishes the limiting free energy in terms of an integral of a family of random variables that are the weak limits of the quenched variances of…
View article: Phase transition in random tensors with multiple independent spikes
Phase transition in random tensors with multiple independent spikes Open
Consider a spiked random tensor obtained as a mixture of two components: noise in the form of a symmetric Gaussian $p$-tensor for $p\geq 3$ and signal in the form of a symmetric low-rank random tensor. The latter is defined as a linear com…
View article: Performance of Bayesian linear regression in a model with mismatch
Performance of Bayesian linear regression in a model with mismatch Open
In this paper we analyze, for a model of linear regression with gaussian covariates, the performance of a Bayesian estimator given by the mean of a log-concave posterior distribution with gaussian prior, in the high-dimensional limit where…
View article: On the Almeida-Thouless transition line in the SK model with centered Gaussian external field
On the Almeida-Thouless transition line in the SK model with centered Gaussian external field Open
We study the phase transition of the free energy in the Sherrington-Kirkpatrick mean-field spin glass model with centered Gaussian external field. We show that the Almeida-Thouless line is the correct transition curve that distinguishes be…
View article: On the Almeida-Thouless transition line in the Sherrington-Kirkpatrick model with centered Gaussian external field
On the Almeida-Thouless transition line in the Sherrington-Kirkpatrick model with centered Gaussian external field Open
We study the phase transition of the free energy in the Sherrington-Kirkpatrick mean-field spin glass model with centered Gaussian external field. We show that the corresponding Almeida-Thouless line is the correct transition curve that di…
View article: On the Almeida-Thouless transition line in the Sherrington-Kirkpatrick model with centered Gaussian external field
On the Almeida-Thouless transition line in the Sherrington-Kirkpatrick model with centered Gaussian external field Open
We study the phase transition of the free energy in the Sherrington-Kirkpatrick mean-field spin glass model with centered Gaussian external field. We show that the corresponding Almeida-Thouless line is the correct transition curve that di…
View article: On $\ell_p$-Gaussian-Grothendieck problem
On $\ell_p$-Gaussian-Grothendieck problem Open
For $p\geq 1$ and $(g_{ij})_{1\leq i,j\leq n}$ being a matrix of i.i.d. standard Gaussian entries, we study the $n$-limit of the $\ell_p$-Gaussian-Grothendieck problem defined as \begin{align*}\max\Bigl\{\sum_{i,j=1}^n g_{ij}x_ix_j: x\in \…
View article: On convergence of Bolthausen's TAP iteration to the local magnetization
On convergence of Bolthausen's TAP iteration to the local magnetization Open
The Thouless, Anderson, and Palmer (TAP) equations state that the local magnetization in the Sherrington-Kirkpatrick mean-field spin glass model satisfies a system of nonlinear equations. In the seminal work [Comm. Math. Phys., 325(1):333-…
View article: Universality of Approximate Message Passing Algorithms
Universality of Approximate Message Passing Algorithms Open
We consider a broad class of Approximate Message Passing (AMP) algorithms defined as a Lipschitzian functional iteration in terms of an $n\times n$ random symmetric matrix $A$. We establish universality in noise for this AMP in the $n$-lim…
View article: Suboptimality of local algorithms for a class of max-cut problems
Suboptimality of local algorithms for a class of max-cut problems Open
We show that in random $K$-uniform hypergraphs of constant average degree,\nfor even $K \\geq 4$, local algorithms defined as factors of i.i.d. can not find\nnearly maximal cuts, when the average degree is sufficiently large. These\nalgori…
View article: Order of Fluctuations of the Free Energy in the SK Model at Critical Temperature
Order of Fluctuations of the Free Energy in the SK Model at Critical Temperature Open
We present an elementary approach to the order of fluctuations for the free energy in the Sherrington-Kirkpatrick mean field spin glass model at and near the critical temperature. It is proved that at the critical temperature the variance …
View article: The generalized TAP free energy
The generalized TAP free energy Open
We consider the mixed $p$-spin mean-field spin glass model with Ising spins and investigate its free energy in the spirit of the TAP approach, named after Thouless, Anderson, and Palmer. More precisely, we define and compute the generalize…
View article: Phase transition in random tensors with multiple spikes
Phase transition in random tensors with multiple spikes Open
University of Minnesota Ph.D. dissertation. 2019. Major: Mathematics. Advisors: Gilad Lerman, Wei-Kuo Chen. 1 computer file (PDF); 102 pages.
View article: Phase transition in the spiked random tensor with Rademacher prior
Phase transition in the spiked random tensor with Rademacher prior Open
We consider the problem of detecting a deformation from a symmetric Gaussian random $p$-tensor $(p\geq 3)$ with a rank-one spike sampled from the Rademacher prior. Recently in Lesieur et al. (2017), it was proved that there exists a critic…
View article: On concentration properties of disordered Hamiltonians
On concentration properties of disordered Hamiltonians Open
We present an elementary approach to concentration of disordered Hamiltonians. Assuming differentiability of the limiting free energy $F$ with respect to the inverse temperature $β$, we show that the Hamiltonian concentrates around the ene…
View article: Disorder chaos in some diluted spin glass models
Disorder chaos in some diluted spin glass models Open
We prove disorder chaos at zero temperature for three types of diluted models with large connectivity parameter: $K$-spin antiferromagnetic Ising model for even $K\geq 2$, $K$-spin spin glass model for even $K\geq 2$, and random $K$-sat mo…
View article: The SK model is infinite step replica symmetry breaking at zero temperature
The SK model is infinite step replica symmetry breaking at zero temperature Open
We prove that the Parisi measure of the mixed p-spin model at zero temperature has infinitely many points in its support. This establishes Parisi's prediction that the functional order parameter of the Sherrington-Kirkpatrick model is not …
View article: On the energy landscape of spherical spin glasses
On the energy landscape of spherical spin glasses Open
We investigate the energy landscape of the spherical mixed even p-spin model near its maximum energy. We relate the distance between pairs of near maxima to the support of the Parisi measure at zero temperature. We then provide an algebrai…
View article: Temperature chaos in some spherical mixed $p$-spin models
Temperature chaos in some spherical mixed $p$-spin models Open
We give two types of examples of the spherical mixed even-$p$-spin models for which chaos in temperature holds. These complement some known results for the spherical pure $p$-spin models and for models with Ising spins. For example, in con…
View article: Parisi formula for the ground state energy in the mixed p-spin model
Parisi formula for the ground state energy in the mixed p-spin model Open
We show that the thermodynamic limit of the ground state energy in the mixed p-spin model can be identified as a variational problem. This gives a natural generalization of the Parisi formula at zero temperature.
View article: A duality principle in spin glasses
A duality principle in spin glasses Open
We prove a duality principle that connects the thermodynamic limits of the free energies of the Hamiltonians and their squared interactions. Under the main assumption that the limiting free energy is concave in the squared temperature para…