Communications on Pure and Applied Mathematics

Article	Citations
The Generalization Error of Random Features Regression: Precise Asymptotics and the Double Descent Curve	58
Global Mild Solutions of the Landau and Non‐Cutoff Boltzmann Equations	37
Global Identifiability of Differential Models	37
Axi‐symmetrization near Point Vortex Solutions for the 2D Euler Equation	22
Transition Threshold for the 3D Couette Flow in Sobolev Space	22
On the Finite Time Blowup of the De Gregorio Model for the 3D Euler Equations	21
Space‐Time Localisation for the Dynamic Model	21
Asymptotic Expansions of Solutions of the Yamabe Equation and the σk‐Yamabe Equation near Isolated Singular Points	21
Liouville Theorems and a Schwarz Lemma for Holomorphic Mappings Between Kähler Manifolds	18
Optimal Transport Based Seismic Inversion:Beyond Cycle Skipping	18
Formation of Shocks for 2D Isentropic Compressible Euler	18
Following the Ground States of Full‐RSB Spherical Spin Glasses	17
Consistent Inversion of Noisy Non‐Abelian X‐Ray Transforms	17
A Riemann‐Hilbert Approach to the Lower Tail of the Kardar‐Parisi‐Zhang Equation	16
On Admissible Locations of Transonic Shock Fronts for Steady Euler Flows in an Almost Flat Finite Nozzle with Prescribed Receiver Pressure	16
Global Well‐Posedness of Master Equations for Deterministic Displacement Convex Potential Mean Field Games	15
For Most Frequencies, Strong Trapping Has a Weak Effect in Frequency‐Domain Scattering	15
Sobolev Inequalities in Manifolds with Nonnegative Curvature	14
The Gauss Image Problem	14
On Ill‐ and Well‐Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations	14
Refined Description and Stability for Singular Solutions of the 2D Keller‐Segel System	13
Well‐Posedness in Gevrey Function Space for 3D Prandtl Equations without Structural Assumption	13
Multitime Distribution in Discrete Polynuclear Growth	12
Gromov‐Hausdorff Limits of Kähler Manifolds with Ricci Curvature Bounded Below II	12
The Batchelor Spectrum of Passive Scalar Turbulence in Stochastic Fluid Mechanics at Fixed Reynolds Number	12

Proof of Modulational Instability of Stokes Waves in Deep Water	11
DLR Equations and Rigidity for the Sine‐Beta Process	11
Navier‐Stokes Equations in Gas Dynamics: Green's Function, Singularity, and Well‐Posedness	11
Uniqueness and Nonuniqueness of Steady States of Aggregation‐Diffusion Equations	11
Inviscid Limit of Vorticity Distributions in the Yudovich Class	11
On the Yau‐Tian‐Donaldson Conjecture for Singular Fano Varieties	10
Log‐Sobolev Inequality for the Continuum Sine‐Gordon Model	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
Ghost Point Diffusion Maps for Solving Elliptic PDEs on Manifolds with Classical Boundary Conditions	9
Unique Asymptotics of Compact Ancient Solutions to Three‐Dimensional Ricci Flow	9
Spatially Inhomogeneous Evolutionary Games	9
Quantitative Estimates for Regular Lagrangian Flows with BV Vector Fields	9
Classification of Generalized Kähler‐Ricci Solitons on Complex Surfaces	8
Homogenization, Linearization, and Large‐Scale Regularity for Nonlinear Elliptic Equations	8
Additivity of Higher Rho Invariants and Nonrigidity of Topological Manifolds	8
The Logarithmic Sobolev Inequality for a Submanifold in Euclidean Space	8
Quantum Corrections to the Pekar Asymptotics of a Strongly Coupled Polaron	8
Finite Time Blowup for the Nematic Liquid Crystal Flow in Dimension Two	7
On the Convex Geometry of Blind Deconvolution and Matrix Completion	7
The Data‐Driven Schrödinger Bridge	7
Formation of Point Shocks for 3D Compressible Euler	7
Mean‐Field and Classical Limit for the N‐Body Quantum Dynamics with Coulomb Interaction	7
KAM Theorem with Normal Frequencies of Finite Limit‐Points for Some Shallow Water Equations	7
Almost‐Rigidity of Frameworks	7
Concentration versus Oscillation Effects in Brittle Damage	7
Quantitative Linearization Results for the Monge‐Ampère Equation	7
Linear Stability of Pipe Poiseuille Flow at High Reynolds Number Regime	7
On the Well‐Posedness of Branched Transportation	6
Generalized TAP Free Energy	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
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
Large‐Scale Analyticity and Unique Continuation for Periodic Elliptic Equations	6
On the Yau‐Tian‐Donaldson Conjecture for Generalized Kähler‐Ricci Soliton Equations	6
Vortex Layers of Small Thickness	6
Restricted Percolation Critical Exponents in High Dimensions	6
Long‐Time Instability of the Couette Flow in Low Gevrey Spaces	6
Likelihood Maximization and Moment Matching in Low SNR Gaussian Mixture Models	5
Arnold Diffusion, Quantitative Estimates, and Stochastic Behavior in the Three‐Body Problem	5
Shock Formation and Vorticity Creation for 3d Euler	5
C2 Regularity of the Surface Tension for the ∇ϕ Interface Model	5
The Regularity of Parametrized Integer Stationary Varifolds in Two Dimensions	5
Birkhoff Normal Form and Long Time Existence for Periodic Gravity Water Waves	5
Isoperimetry, Scalar Curvature, and Mass in Asymptotically Flat Riemannian 3‐Manifolds	5
On the Relationship Between the Thin Film Equation and Tanner's Law	5
A High‐Order Integral Equation‐Based Solver for the Time‐Dependent Schrödinger Equation	5
Chord measures in integral geometry and their Minkowski problems	5
Unique Continuation at the Boundary for Harmonic Functions in C1 Domains and Lipschitz Domains with Small Constant	5

Plateau's Problem as a Singular Limit of Capillarity Problems	5
Likelihood landscape and maximum likelihood estimation for the discrete orbit recovery model	5
Maximum of the Characteristic Polynomial for a Random Permutation Matrix	5
Maximum and Shape of Interfaces in 3D Ising Crystals	5
Sub‐Gaussian Matrices on Sets: Optimal Tail Dependence and Applications	5
The Continuous‐Time Lace Expansion	5
Soliton versus the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation	5
Improved Moser‐Trudinger‐Onofri Inequality under Constraints	5
A Remark on the Concentration Compactness Principle in Critical Dimension	4
Rigorous data‐driven computation of spectral properties of Koopman operators for dynamical systems	4
Log‐Sobolev inequality for the φ24$\varphi ^4_2$ and φ34$\varphi ^4_3$ measures	4
Optimal Symplectic Connections on Holomorphic Submersions	4
Strong Stability for the Wulff Inequality with a Crystalline Norm	4
Isotropic‐Nematic Phase Transition and Liquid Crystal Droplets	4
Fast Computation of Orthogonal Systems with a Skew‐Symmetric Differentiation Matrix	4
Global minimizers of a large class of anisotropic attractive‐repulsive interaction energies in 2D	4
Mean Convex Mean Curvature Flow with Free Boundary	4
Mathematical Modeling and Analysis of Spatial Neuron Dynamics: Dendritic Integration and Beyond	4
Maximal Hypersurfaces over Exterior Domains	4
A Talenti Comparison Result for Solutions to Elliptic Problems with Robin Boundary Conditions	4
Dissipative Euler Flows for Vortex Sheet Initial Data without Distinguished Sign	4
Separable Hamiltonian PDEs and Turning Point Principle for Stability of Gaseous Stars	4
Existence and Uniqueness of Green's Functions to Nonlinear Yamabe Problems	4
Minimizers for the Thin One‐Phase Free Boundary Problem	4
Emergence of Concentration Effects in the Variational Analysis of theN‐Clock Model	4
Prescribing Morse Scalar Curvatures: Pinching and Morse Theory	3
Finite‐Rank Perturbations of Random Band Matrices via Infinitesimal Free Probability	3
Variational Embedding for Quantum Many‐Body Problems	3
Upper Tail Large Deviations of Regular Subgraph Counts in Erdős‐Rényi Graphs in the Full Localized Regime	3
Strict Inequality for the Chemical Distance Exponent in Two‐Dimensional Critical Percolation	3
Viscosity Limits for Zeroth‐Order Pseudodifferential Operators	3
Water‐Waves Problem with Surface Tension in a Corner Domain II: The Local Well‐Posedness	3
Validity of steady Prandtl layer expansions	3
Continued Fractions and Hankel Determinants from Hyperelliptic Curves	3
Contact points with integer frequencies in the thin obstacle problem	3
The anisotropic min‐max theory: Existence of anisotropic minimal and CMC surfaces	3
A Functional Central Limit Theorem for Polaron Path Measures	3
Asymptotic Stability of Harmonic Maps on the Hyperbolic Plane under the Schrödinger Maps Evolution	3
Uniqueness of Two‐Bubble Wave Maps in High Equivariance Classes	3
On the stabilizing effect of rotation in the 3d Euler equations	3
Gaussian Regularization of the Pseudospectrum and Davies’ Conjecture	3
Area‐Minimizing Currents mod 2Q: Linear Regularity Theory	3
Moderately Discontinuous Homology	3
A Scalar Version of the Caflisch‐Luke Paradox	3
Optimal Small Scale Equidistribution of Lattice Points on the Sphere, Heegner Points, and Closed Geodesics	2
Cycle Class Maps and Birational Invariants	2
Pure gravity traveling quasi‐periodic water waves with constant vorticity	2
Fast Reaction Limit with Nonmonotone Reaction Function	2
Upper Tail Large Deviations in First Passage Percolation	2
Corrigendum and Addendum: Identification of the Polaron Measure I: Fixed Coupling Regime and the Central Limit Theorem for Large Times	2
Vortex Filament Solutions of the Navier‐Stokes Equations	2
Fermi isospectrality for discrete periodic Schrödinger operators	2
Optimal Error Estimates for Analytic Continuation in the Upper Half‐Plane	2
Nonlinear inviscid damping and shear‐buoyancy instability in the two‐dimensional Boussinesq equations	2
Global well‐posedness for the one‐phase Muskat problem	2
Compressible Navier‐Stokes equations with ripped density	2
The One‐Dimensional Log‐Gas Free Energy Has a Unique Minimizer	2
Universality Near the Gradient Catastrophe Point in the Semiclassical Sine‐Gordon Equation	2
The stationary AKPZ equation: Logarithmic superdiffusivity	2
Traveling Wave Solutions to the Free Boundary Incompressible Navier‐Stokes Equations	2
The maximum of log‐correlated Gaussian fields in random environment	2
Log‐Sobolev inequality for near critical Ising models	2
Reflective prolate‐spheroidal operators and the adelic Grassmannian	2
Sharp asymptotic estimates for expectations, probabilities, and mean first passage times in stochastic systems with small noise	2
Minimal Surfaces in Hyperbolic 3‐Manifolds	2
Sine‐kernel determinant on two large intervals	2
Existence of multi‐dimensional contact discontinuities for the ideal compressible magnetohydrodynamics	2
Long‐Term Regularity of 3D Gravity Water Waves	2
The Sphere Covering Inequality and Its Dual	2
Well‐posedness of stochastic heat equation with distributional drift and skew stochastic heat equation	2
Coagulation‐Fragmentation Equations with Multiplicative Coagulation Kernel and Constant Fragmentation Kernel	2
A scaling limit of the parabolic Anderson model with exclusion interaction	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
Free boundary partial regularity in the thin obstacle problem	1
Strong Asymptotics of Planar Orthogonal Polynomials: Gaussian Weight Perturbed by Finite Number of Point Charges	1
Online Prediction with History‐Dependent Experts: The General Case	1
A Driven Tagged Particle in Symmetric Exclusion Processes with Removals	1
Logarithmic cotangent bundles, Chern‐Mather classes, and the Huh‐Sturmfels involution conjecture	1
Large deviations principle for the cubic NLS equation	1

The Brownian Castle	1
C2,α$C^{2,\alpha }$ regularity of free boundaries in optimal transportation	1
Global solutions of the compressible Euler‐Poisson equations with large initial data of spherical symmetry	1
A 2‐component Camassa‐Holm Equation, Euler‐Bernoulli Beam Problem, and Noncommutative Continued Fractions	1
A generalization of Geroch's conjecture	1
A Relative Entropy and a Unique Continuation Result for Ricci Expanders	1
Regularity of Free Boundary Minimal Surfaces in Locally Polyhedral Domains	1
Magnetic slowdown of topological edge states	1
Magnetic helicity, weak solutions and relaxation of ideal MHD	1
Spectrum of random d‐regular graphs up to the edge	1
Shattering versus metastability in spin glasses	1
Robustness of Liouville Measure under a Family of Stable Diffusions	1
Hearing the shape of ancient noncollapsed flows in R4$\mathbb {R}^{4}$	1
Landscape complexity beyond invariance and the elastic manifold	1
Existence of constant mean curvature 2‐Spheres in Riemannian 3‐spheres	1
Stability of Hill's spherical vortex	1
Compressive phase retrieval: Optimal sample complexity with deep generative priors	1
A dynamical approach to the study of instability near Couette flow	1
Detecting the birth and death of finite‐time coherent sets	1
Thermodynamic limit of the first Lee‐Yang zero	1
On Heavy‐Tail Phenomena in Some Large‐Deviations Problems	1
Critical sets of solutions of elliptic equations in periodic homogenization	1
Prescribed curvature measure problem in hyperbolic space	1
Corrigendum: Quasiconvex Elastodynamics: Weak‐Strong Uniqueness for Measure‐Valued Solutions	1
Conditional Density Estimation, Latent Variable Discovery, and Optimal Transport	1
An Extremal Problem Arising in the Dynamics of Two‐Phase Materials That Directly Reveals Information about the Internal Geometry	1
Singularities almost always scatter: Regularity results for non‐scattering inhomogeneities	1
Sigma Delta Quantization for Images	1
Convergence of the self‐dual U(1)‐Yang–Mills–Higgs energies to the (n−2)$(n-2)$‐area functional	1
Universality for the Conjugate Gradient and MINRES Algorithms on Sample Covariance Matrices	1
Local Flexibility for Open Partial Differential Relations	1
Plateau's Problem as a Singular Limit of Capillarity Problems	1
The Bessel kernel determinant on large intervals and Birkhoff's ergodic theorem	1
High‐dimensional limit theorems for SGD: Effective dynamics and critical scaling	1
Conformal covariance of connection probabilities and fields in 2D critical percolation	1
Plateau's Problem as a Singular Limit of Capillarity Problems	1
Ballistic Transport for One‐Dimensional Quasiperiodic Schrödinger Operators	1
Critical local well‐posedness for the fully nonlinear Peskin problem	1
A Control Variate Method Driven by Diffusion Approximation	1