Communications on Pure and Applied Mathematics

Article	Citations
The Generalization Error of Random Features Regression: Precise Asymptotics and the Double Descent Curve	55
Global Identifiability of Differential Models	38
Global Mild Solutions of the Landau and Non‐Cutoff Boltzmann Equations	36
Random Band Matrices in the Delocalized Phase I: Quantum Unique Ergodicity and Universality	22
On the Integrability of the Benjamin‐Ono Equation on the Torus	21
Space‐Time Localisation for the Dynamic Model	20
On the Finite Time Blowup of the De Gregorio Model for the 3D Euler Equations	20
Transition Threshold for the 3D Couette Flow in Sobolev Space	19
Asymptotic Expansions of Solutions of the Yamabe Equation and the σk‐Yamabe Equation near Isolated Singular Points	19
Axi‐symmetrization near Point Vortex Solutions for the 2D Euler Equation	19
Optimal Transport Based Seismic Inversion:Beyond Cycle Skipping	17
Consistent Inversion of Noisy Non‐Abelian X‐Ray Transforms	17
Liouville Theorems and a Schwarz Lemma for Holomorphic Mappings Between Kähler Manifolds	16
Formation of Shocks for 2D Isentropic Compressible Euler	16
Following the Ground States of Full‐RSB Spherical Spin Glasses	16
For Most Frequencies, Strong Trapping Has a Weak Effect in Frequency‐Domain Scattering	15
A Riemann‐Hilbert Approach to the Lower Tail of the Kardar‐Parisi‐Zhang Equation	14
Global Well‐Posedness of Master Equations for Deterministic Displacement Convex Potential Mean Field Games	14
The Gauss Image Problem	14
On Ill‐ and Well‐Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations	13
Well‐Posedness in Gevrey Function Space for 3D Prandtl Equations without Structural Assumption	13
Refined Description and Stability for Singular Solutions of the 2D Keller‐Segel System	12
On Admissible Locations of Transonic Shock Fronts for Steady Euler Flows in an Almost Flat Finite Nozzle with Prescribed Receiver Pressure	12
Gromov‐Hausdorff Limits of Kähler Manifolds with Ricci Curvature Bounded Below II	12
Multitime Distribution in Discrete Polynuclear Growth	12

Sobolev Inequalities in Manifolds with Nonnegative Curvature	12
Proof of Modulational Instability of Stokes Waves in Deep Water	11
The Batchelor Spectrum of Passive Scalar Turbulence in Stochastic Fluid Mechanics at Fixed Reynolds Number	11
DLR Equations and Rigidity for the Sine‐Beta Process	11
Inviscid Limit of Vorticity Distributions in the Yudovich Class	11
Navier‐Stokes Equations in Gas Dynamics: Green's Function, Singularity, and Well‐Posedness	10
On the Yau‐Tian‐Donaldson Conjecture for Singular Fano Varieties	10
Uniqueness and Nonuniqueness of Steady States of Aggregation‐Diffusion Equations	10
Spatially Inhomogeneous Evolutionary Games	9
Central Limit Theorem for Linear Eigenvalue Statistics of Non‐Hermitian Random Matrices	9
Trainability and Accuracy of Artificial Neural Networks: An Interacting Particle System Approach	9
Quantitative Estimates for Regular Lagrangian Flows with BV Vector Fields	9
Log‐Sobolev Inequality for the Continuum Sine‐Gordon Model	9
Ghost Point Diffusion Maps for Solving Elliptic PDEs on Manifolds with Classical Boundary Conditions	9
From 1 to 6: A Finer Analysis of Perturbed Branching Brownian Motion	8
Homogenization, Linearization, and Large‐Scale Regularity for Nonlinear Elliptic Equations	8
Classification of Generalized Kähler‐Ricci Solitons on Complex Surfaces	8
The Logarithmic Sobolev Inequality for a Submanifold in Euclidean Space	8
Unique Asymptotics of Compact Ancient Solutions to Three‐Dimensional Ricci Flow	8
Additivity of Higher Rho Invariants and Nonrigidity of Topological Manifolds	8
KAM Theorem with Normal Frequencies of Finite Limit‐Points for Some Shallow Water Equations	7
On the Convex Geometry of Blind Deconvolution and Matrix Completion	7
Quantum Corrections to the Pekar Asymptotics of a Strongly Coupled Polaron	7
Mean‐Field and Classical Limit for the N‐Body Quantum Dynamics with Coulomb Interaction	7
Almost‐Rigidity of Frameworks	7
Vortex Layers of Small Thickness	6
Regularized Stokes Immersed Boundary Problems in Two Dimensions: Well‐Posedness, Singular Limit, and Error Estimates	6
Refined Asymptotic Behavior of Blowup Solutions to a Simplified Chemotaxis System	6
On the Yau‐Tian‐Donaldson Conjecture for Generalized Kähler‐Ricci Soliton Equations	6
Linear Stability of Pipe Poiseuille Flow at High Reynolds Number Regime	6
Generalized TAP Free Energy	6
Restricted Percolation Critical Exponents in High Dimensions	6
Large‐Scale Analyticity and Unique Continuation for Periodic Elliptic Equations	6
Real Analytic Local Well‐Posedness for the Triple Deck	6
On the Well‐Posedness of Branched Transportation	6
The Quasi Curvature‐Dimension Condition with Applications to Sub‐Riemannian Manifolds	6
Entropy‐Bounded Solutions to the One‐Dimensional Heat Conductive Compressible Navier‐Stokes Equations with Far Field Vacuum	6
Finite Time Blowup for the Nematic Liquid Crystal Flow in Dimension Two	6
Concentration versus Oscillation Effects in Brittle Damage	6
Quantitative Linearization Results for the Monge‐Ampère Equation	6
The Data‐Driven Schrödinger Bridge	6
Maximum and Shape of Interfaces in 3D Ising Crystals	5
On the Relationship Between the Thin Film Equation and Tanner's Law	5
Long‐Time Instability of the Couette Flow in Low Gevrey Spaces	5
Unique Continuation at the Boundary for Harmonic Functions in C1 Domains and Lipschitz Domains with Small Constant	5
Improved Moser‐Trudinger‐Onofri Inequality under Constraints	5
Maximum of the Characteristic Polynomial for a Random Permutation Matrix	5
Arnold Diffusion, Quantitative Estimates, and Stochastic Behavior in the Three‐Body Problem	5
A High‐Order Integral Equation‐Based Solver for the Time‐Dependent Schrödinger Equation	5
The Regularity of Parametrized Integer Stationary Varifolds in Two Dimensions	5

Formation of Point Shocks for 3D Compressible Euler	5
Sub‐Gaussian Matrices on Sets: Optimal Tail Dependence and Applications	5
The Continuous‐Time Lace Expansion	5
Plateau's Problem as a Singular Limit of Capillarity Problems	5
Minimizers for the Thin One‐Phase Free Boundary Problem	4
Isoperimetry, Scalar Curvature, and Mass in Asymptotically Flat Riemannian 3‐Manifolds	4
A Talenti Comparison Result for Solutions to Elliptic Problems with Robin Boundary Conditions	4
Shock Formation and Vorticity Creation for 3d Euler	4
Global minimizers of a large class of anisotropic attractive‐repulsive interaction energies in 2D	4
Likelihood landscape and maximum likelihood estimation for the discrete orbit recovery model	4
Maximal Hypersurfaces over Exterior Domains	4
Likelihood Maximization and Moment Matching in Low SNR Gaussian Mixture Models	4
A Remark on the Concentration Compactness Principle in Critical Dimension	4
Soliton versus the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation	4
Optimal Symplectic Connections on Holomorphic Submersions	4
Birkhoff Normal Form and Long Time Existence for Periodic Gravity Water Waves	4
Emergence of Concentration Effects in the Variational Analysis of theN‐Clock Model	4
Fast Computation of Orthogonal Systems with a Skew‐Symmetric Differentiation Matrix	4
Separable Hamiltonian PDEs and Turning Point Principle for Stability of Gaseous Stars	4
Log‐Sobolev inequality for the φ24$\varphi ^4_2$ and φ34$\varphi ^4_3$ measures	4
C2 Regularity of the Surface Tension for the ∇ϕ Interface Model	4
Existence and Uniqueness of Green's Functions to Nonlinear Yamabe Problems	4
Mathematical Modeling and Analysis of Spatial Neuron Dynamics: Dendritic Integration and Beyond	3
Continued Fractions and Hankel Determinants from Hyperelliptic Curves	3
Gaussian Regularization of the Pseudospectrum and Davies’ Conjecture	3
Strict Inequality for the Chemical Distance Exponent in Two‐Dimensional Critical Percolation	3
On the Stability of Solitary Water Waves with a Point Vortex	3
Rigorous data‐driven computation of spectral properties of Koopman operators for dynamical systems	3
A Scalar Version of the Caflisch‐Luke Paradox	3
Strong Stability for the Wulff Inequality with a Crystalline Norm	3
Finite‐Rank Perturbations of Random Band Matrices via Infinitesimal Free Probability	3
On the stabilizing effect of rotation in the 3d Euler equations	3
Chord measures in integral geometry and their Minkowski problems	3
Viscosity Limits for Zeroth‐Order Pseudodifferential Operators	3
Mean Convex Mean Curvature Flow with Free Boundary	3
Dissipative Euler Flows for Vortex Sheet Initial Data without Distinguished Sign	3
Water‐Waves Problem with Surface Tension in a Corner Domain II: The Local Well‐Posedness	3
Uniqueness of Two‐Bubble Wave Maps in High Equivariance Classes	3
Isotropic‐Nematic Phase Transition and Liquid Crystal Droplets	3
Variational Embedding for Quantum Many‐Body Problems	3
Area‐Minimizing Currents mod 2Q: Linear Regularity Theory	3
A Functional Central Limit Theorem for Polaron Path Measures	3
Moderately Discontinuous Homology	3
Asymptotic Stability of Harmonic Maps on the Hyperbolic Plane under the Schrödinger Maps Evolution	3
Log‐Sobolev inequality for near critical Ising models	2
The anisotropic min‐max theory: Existence of anisotropic minimal and CMC surfaces	2
Optimal Small Scale Equidistribution of Lattice Points on the Sphere, Heegner Points, and Closed Geodesics	2
Sine‐kernel determinant on two large intervals	2
Prescribing Morse Scalar Curvatures: Pinching and Morse Theory	2
Pure gravity traveling quasi‐periodic water waves with constant vorticity	2
Universality Near the Gradient Catastrophe Point in the Semiclassical Sine‐Gordon Equation	2
The stationary AKPZ equation: Logarithmic superdiffusivity	2
Coagulation‐Fragmentation Equations with Multiplicative Coagulation Kernel and Constant Fragmentation Kernel	2
Upper Tail Large Deviations of Regular Subgraph Counts in Erdős‐Rényi Graphs in the Full Localized Regime	2
Uniformly Positive Correlations in the Dimer Model and Macroscopic Interacting Self‐Avoiding Walk in ℤd, d ≥ 3	2
Long‐time correlations for a hard‐sphere gas at equilibrium	2
Global well‐posedness for the one‐phase Muskat problem	2
The One‐Dimensional Log‐Gas Free Energy Has a Unique Minimizer	2
Long‐Term Regularity of 3D Gravity Water Waves	2
The Sphere Covering Inequality and Its Dual	2
Corrigendum and Addendum: Identification of the Polaron Measure I: Fixed Coupling Regime and the Central Limit Theorem for Large Times	2
Reflective prolate‐spheroidal operators and the adelic Grassmannian	2
Fermi isospectrality for discrete periodic Schrödinger operators	2
Optimal Error Estimates for Analytic Continuation in the Upper Half‐Plane	2
Sharp asymptotic estimates for expectations, probabilities, and mean first passage times in stochastic systems with small noise	2
Compressible Navier‐Stokes equations with ripped density	2
Validity of steady Prandtl layer expansions	2
Fast Reaction Limit with Nonmonotone Reaction Function	2
Upper Tail Large Deviations in First Passage Percolation	2
Traveling Wave Solutions to the Free Boundary Incompressible Navier‐Stokes Equations	2
The maximum of log‐correlated Gaussian fields in random environment	2
The Bessel kernel determinant on large intervals and Birkhoff's ergodic theorem	1
Plateau's Problem as a Singular Limit of Capillarity Problems	1
Conformal covariance of connection probabilities and fields in 2D critical percolation	1
Critical local well‐posedness for the fully nonlinear Peskin problem	1
Ballistic Transport for One‐Dimensional Quasiperiodic Schrödinger Operators	1
An Extremal Problem Arising in the Dynamics of Two‐Phase Materials That Directly Reveals Information about the Internal Geometry	1
A Control Variate Method Driven by Diffusion Approximation	1
Strong Asymptotics of Planar Orthogonal Polynomials: Gaussian Weight Perturbed by Finite Number of Point Charges	1
Logarithmic cotangent bundles, Chern‐Mather classes, and the Huh‐Sturmfels involution conjecture	1

Cycle Class Maps and Birational Invariants	1
Stability of Hill's spherical vortex	1
A scaling limit of the parabolic Anderson model with exclusion interaction	1
Compressive phase retrieval: Optimal sample complexity with deep generative priors	1
A Driven Tagged Particle in Symmetric Exclusion Processes with Removals	1
Detecting the birth and death of finite‐time coherent sets	1
The Brownian Castle	1
A 2‐component Camassa‐Holm Equation, Euler‐Bernoulli Beam Problem, and Noncommutative Continued Fractions	1
Global solutions of the compressible Euler‐Poisson equations with large initial data of spherical symmetry	1
A Relative Entropy and a Unique Continuation Result for Ricci Expanders	1
A generalization of Geroch's conjecture	1
Magnetic slowdown of topological edge states	1
Regularity of Free Boundary Minimal Surfaces in Locally Polyhedral Domains	1
Singularities almost always scatter: Regularity results for non‐scattering inhomogeneities	1
Universality for the Conjugate Gradient and MINRES Algorithms on Sample Covariance Matrices	1
Minimal Surfaces in Hyperbolic 3‐Manifolds	1
Online Prediction with History‐Dependent Experts: The General Case	1
Convergence of the self‐dual U(1)‐Yang–Mills–Higgs energies to the (n−2)$(n-2)$‐area functional	1
Large deviations principle for the cubic NLS equation	1
Plateau's Problem as a Singular Limit of Capillarity Problems	1
Existence of constant mean curvature 2‐Spheres in Riemannian 3‐spheres	1
High‐dimensional limit theorems for SGD: Effective dynamics and critical scaling	1
Sigma Delta Quantization for Images	1
On Heavy‐Tail Phenomena in Some Large‐Deviations Problems	1
Thermodynamic limit of the first Lee‐Yang zero	1
Prescribed curvature measure problem in hyperbolic space	1
Critical sets of solutions of elliptic equations in periodic homogenization	1
Conditional Density Estimation, Latent Variable Discovery, and Optimal Transport	1
Corrigendum: Quasiconvex Elastodynamics: Weak‐Strong Uniqueness for Measure‐Valued Solutions	1
Free boundary partial regularity in the thin obstacle problem	1
Well‐posedness of stochastic heat equation with distributional drift and skew stochastic heat equation	1
Shattering versus metastability in spin glasses	1
Robustness of Liouville Measure under a Family of Stable Diffusions	1
Contact points with integer frequencies in the thin obstacle problem	1
Landscape complexity beyond invariance and the elastic manifold	1
Vortex Filament Solutions of the Navier‐Stokes Equations	1
C2,α$C^{2,\alpha }$ regularity of free boundaries in optimal transportation	1
Local Flexibility for Open Partial Differential Relations	1
Nonlinear inviscid damping and shear‐buoyancy instability in the two‐dimensional Boussinesq equations	1