Communications on Pure and Applied Mathematics

Article	Citations
The Generalization Error of Random Features Regression: Precise Asymptotics and the Double Descent Curve	66
Axi‐symmetrization near Point Vortex Solutions for the 2D Euler Equation	24
Optimal Transport Based Seismic Inversion:Beyond Cycle Skipping	23
On the Finite Time Blowup of the De Gregorio Model for the 3D Euler Equations	23
Global Well‐Posedness of Master Equations for Deterministic Displacement Convex Potential Mean Field Games	22
Liouville Theorems and a Schwarz Lemma for Holomorphic Mappings Between Kähler Manifolds	19
Sobolev Inequalities in Manifolds with Nonnegative Curvature	19
A Riemann‐Hilbert Approach to the Lower Tail of the Kardar‐Parisi‐Zhang Equation	18
On Ill‐ and Well‐Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations	17
On Admissible Locations of Transonic Shock Fronts for Steady Euler Flows in an Almost Flat Finite Nozzle with Prescribed Receiver Pressure	17
Well‐Posedness in Gevrey Function Space for 3D Prandtl Equations without Structural Assumption	16
The Batchelor Spectrum of Passive Scalar Turbulence in Stochastic Fluid Mechanics at Fixed Reynolds Number	16
Refined Description and Stability for Singular Solutions of the 2D Keller‐Segel System	16
Rigorous data‐driven computation of spectral properties of Koopman operators for dynamical systems	15
Multitime Distribution in Discrete Polynuclear Growth	14
Trainability and Accuracy of Artificial Neural Networks: An Interacting Particle System Approach	14
Proof of Modulational Instability of Stokes Waves in Deep Water	13
Central Limit Theorem for Linear Eigenvalue Statistics of Non‐Hermitian Random Matrices	12
DLR Equations and Rigidity for the Sine‐Beta Process	11
Formation of Point Shocks for 3D Compressible Euler	10
Shock Formation and Vorticity Creation for 3d Euler	10
Navier‐Stokes Equations in Gas Dynamics: Green's Function, Singularity, and Well‐Posedness	10
Quantitative Estimates for Regular Lagrangian Flows withBVVector Fields	10
Mean‐Field and Classical Limit for the N‐Body Quantum Dynamics with Coulomb Interaction	10
The Data‐Driven Schrödinger Bridge	9

Spatially Inhomogeneous Evolutionary Games	9
Additivity of Higher Rho Invariants and Nonrigidity of Topological Manifolds	9
Ghost Point Diffusion Maps for Solving Elliptic PDEs on Manifolds with Classical Boundary Conditions	9
Linear Stability of Pipe Poiseuille Flow at High Reynolds Number Regime	9
Finite Time Blowup for the Nematic Liquid Crystal Flow in Dimension Two	8
Validity of steady Prandtl layer expansions	8
Long‐Time Instability of the Couette Flow in Low Gevrey Spaces	8
Entropy‐Bounded Solutions to the One‐Dimensional Heat Conductive Compressible Navier‐Stokes Equations with Far Field Vacuum	8
Quantitative Linearization Results for theMonge‐AmpèreEquation	8
Generalized TAP Free Energy	7
Gaussian Regularization of the Pseudospectrum and Davies’ Conjecture	7
On the Yau‐Tian‐Donaldson Conjecture for Generalized Kähler‐Ricci Soliton Equations	7
Almost‐Rigidity of Frameworks	7
Dissipative Euler Flows for Vortex Sheet Initial Data without Distinguished Sign	7
Isoperimetry, Scalar Curvature, and Mass in Asymptotically Flat Riemannian 3‐Manifolds	7
Soliton versus the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation	7
Likelihood Maximization and Moment Matching in Low SNR Gaussian Mixture Models	6
Arnold Diffusion, Quantitative Estimates, and Stochastic Behavior in the Three‐Body Problem	6
C2 Regularity of the Surface Tension for the ∇ϕ Interface Model	6
Pure gravity traveling quasi‐periodic water waves with constant vorticity	6
A Talenti Comparison Result for Solutions to Elliptic Problems with Robin Boundary Conditions	6
Separable Hamiltonian PDEs and Turning Point Principle for Stability of Gaseous Stars	6
Unique Continuation at the Boundary for Harmonic Functions in C1 Domains and Lipschitz Domains with Small Constant	6
Regularized Stokes Immersed Boundary Problems in Two Dimensions: Well‐Posedness, Singular Limit, and Error Estimates	6
Sub‐Gaussian Matrices on Sets: Optimal Tail Dependence and Applications	6
Nonlinear inviscid damping and shear‐buoyancy instability in the two‐dimensional Boussinesq equations	6
The Quasi Curvature‐Dimension Condition with Applications to Sub‐Riemannian Manifolds	6
Maximum and Shape of Interfaces in 3D Ising Crystals	5
Log‐Sobolev inequality for the φ24$\varphi ^4_2$ and φ34$\varphi ^4_3$ measures	5
Birkhoff Normal Form and Long Time Existence for Periodic Gravity Water Waves	5
Mathematical Modeling and Analysis of Spatial Neuron Dynamics: Dendritic Integration and Beyond	5
A Remark on the Concentration Compactness Principle in Critical Dimension	5
The Continuous‐Time Lace Expansion	5
Long‐Term Regularity of 3D Gravity Water Waves	5
Isotropic‐Nematic Phase Transition and Liquid Crystal Droplets	5
Viscosity Limits for Zeroth‐Order Pseudodifferential Operators	5
Likelihood landscape and maximum likelihood estimation for the discrete orbit recovery model	5
Fast Reaction Limit with Nonmonotone Reaction Function	5
Uniqueness of Two‐Bubble Wave Maps in High Equivariance Classes	4
Variational Embedding for Quantum Many‐Body Problems	4
Chord measures in integral geometry and their Minkowski problems	4
Mean Convex Mean Curvature Flow with Free Boundary	4
Existence and Uniqueness of Green's Functions to Nonlinear Yamabe Problems	4
Minimizers for the Thin One‐Phase Free Boundary Problem	4
Fast Computation of Orthogonal Systems with a Skew‐Symmetric Differentiation Matrix	4
Area‐Minimizing Currents mod 2Q: Linear Regularity Theory	4
Upper Tail Large Deviations of Regular Subgraph Counts in Erdős‐Rényi Graphs in the Full Localized Regime	4
Universality Near the Gradient Catastrophe Point in the Semiclassical Sine‐Gordon Equation	4
Emergence of Concentration Effects in the Variational Analysis of theN‐Clock Model	4
Traveling Wave Solutions to the Free Boundary Incompressible Navier‐Stokes Equations	4

Fermi isospectrality for discrete periodic Schrödinger operators	4
Asymptotic Stability of Harmonic Maps on the Hyperbolic Plane under the Schrödinger Maps Evolution	4
The anisotropic min‐max theory: Existence of anisotropic minimal and CMC surfaces	3
Existence of multi‐dimensional contact discontinuities for the ideal compressible magnetohydrodynamics	3
A scaling limit of the parabolic Anderson model with exclusion interaction	3
Fully Nonlinear Equations with Applications to Grad Equations in Plasma Physics	3
On the stabilizing effect of rotation in the 3d Euler equations	3
A Scalar Version of the Caflisch‐Luke Paradox	3
Uniformly Positive Correlations in the Dimer Model and Macroscopic Interacting Self‐Avoiding Walk in ℤd, d ≥ 3	3
Singularities almost always scatter: Regularity results for non‐scattering inhomogeneities	3
Plateau's Problem as a Singular Limit of Capillarity Problems	3
Prescribing Morse Scalar Curvatures: Pinching and Morse Theory	3
Regularity of Free Boundary Minimal Surfaces in Locally Polyhedral Domains	3
Sharp asymptotic estimates for expectations, probabilities, and mean first passage times in stochastic systems with small noise	3
Detecting the birth and death of finite‐time coherent sets	3
Global minimizers of a large class of anisotropic attractive‐repulsive interaction energies in 2D	3
Vortex Filament Solutions of the Navier‐Stokes Equations	3
Compressible Navier‐Stokes equations with ripped density	3
Hearing the shape of ancient noncollapsed flows in R4$\mathbb {R}^{4}$	3
A Functional Central Limit Theorem for Polaron Path Measures	3
A dynamical approach to the study of instability near Couette flow	3
Contact points with integer frequencies in the thin obstacle problem	3
Magnetic slowdown of topological edge states	3
Log‐Sobolev inequality for near critical Ising models	3
Strong Asymptotics of Planar Orthogonal Polynomials: Gaussian Weight Perturbed by Finite Number of Point Charges	3
Moderately Discontinuous Homology	3
Minimal Surfaces in Hyperbolic 3‐Manifolds	2
Stationary measure for the open KPZ equation	2
Global solutions of the compressible Euler‐Poisson equations with large initial data of spherical symmetry	2
A generalization of Geroch's conjecture	2
Ballistic Transport for One‐Dimensional Quasiperiodic Schrödinger Operators	2
The stationary AKPZ equation: Logarithmic superdiffusivity	2
Upper Tail Large Deviations in First Passage Percolation	2
Coagulation‐Fragmentation Equations with Multiplicative Coagulation Kernel and Constant Fragmentation Kernel	2
Long‐time correlations for a hard‐sphere gas at equilibrium	2
Fluctuation exponents of the KPZ equation on a large torus	2
Long range order for random field Ising and Potts models	2
Stability of the tangent bundle through conifold transitions	2
Sine‐kernel determinant on two large intervals	2
The Brownian Castle	2
On the Maxwell‐Bloch system in the sharp‐line limit without solitons	2
Conformal covariance of connection probabilities and fields in 2D critical percolation	2
Variational methods for a singular SPDE yielding the universality of the magnetization ripple	2
Well‐posedness of stochastic heat equation with distributional drift and skew stochastic heat equation	2
Magnetic helicity, weak solutions and relaxation of ideal MHD	2
On the incompressible limit for a tumour growth model incorporating convective effects	2
Reflective prolate‐spheroidal operators and the adelic Grassmannian	2
Global well‐posedness for the one‐phase Muskat problem	2
Cycle Class Maps and Birational Invariants	2
Existence of constant mean curvature 2‐Spheres in Riemannian 3‐spheres	2
The One‐Dimensional Log‐Gas Free Energy Has a Unique Minimizer	2
Regularity for convex viscosity solutions of special Lagrangian equation	2
A Control Variate Method Driven by Diffusion Approximation	2
Stability of Hill's spherical vortex	2
Logarithmic cotangent bundles, Chern‐Mather classes, and the Huh‐Sturmfels involution conjecture	2
Corrigendum and Addendum: Identification of the Polaron Measure I: Fixed Coupling Regime and the Central Limit Theorem for Large Times	2
The maximum of log‐correlated Gaussian fields in random environment	2
Giant component for the supercritical level‐set percolation of the Gaussian free field on regular expander graphs	2
Optimal Small Scale Equidistribution of Lattice Points on the Sphere, Heegner Points, and Closed Geodesics	2
Local Flexibility for Open Partial Differential Relations	1
Online Prediction with History‐Dependent Experts: The General Case	1
Critical sets of solutions of elliptic equations in periodic homogenization	1
Integrability of SLE via conformal welding of random surfaces	1
Convergence of the self‐dual U(1)‐Yang–Mills–Higgs energies to the (n−2)$(n-2)$‐area functional	1
Global regularity for critical SQG in bounded domains	1
Phase diagram and topological expansion in the complex quartic random matrix model	1
High‐dimensional limit theorems for SGD: Effective dynamics and critical scaling	1
Conditional Density Estimation, Latent Variable Discovery, and Optimal Transport	1
Leapfrogging vortex rings for the three‐dimensional incompressible Euler equations	1
The forbidden region for random zeros: Appearance of quadrature domains	1
Critical local well‐posedness for the fully nonlinear Peskin problem	1
Soft Riemann‐Hilbert problems and planar orthogonal polynomials	1
Spectrum of random d‐regular graphs up to the edge	1
Discrete honeycombs, rational edges, and edge states	1
Thermodynamic limit of the first Lee‐Yang zero	1
Universality for the Conjugate Gradient and MINRES Algorithms on Sample Covariance Matrices	1
Non‐degenerate minimal submanifolds as energy concentration sets: A variational approach	1
SISTA: Learning Optimal Transport Costs under Sparsity Constraints	1
C2,α$C^{2,\alpha }$ regularity of free boundaries in optimal transportation	1
Overcrowding and separation estimates for the Coulomb gas	1

A 2‐component Camassa‐Holm Equation, Euler‐Bernoulli Beam Problem, and Noncommutative Continued Fractions	1
Plateau's Problem as a Singular Limit of Capillarity Problems	1
Inhomogeneous turbulence for the Wick Nonlinear Schrödinger equation	1
Free boundary partial regularity in the thin obstacle problem	1
Constrained deformations of positive scalar curvature metrics, II	1
Shattering versus metastability in spin glasses	1
The Calogero–Moser derivative nonlinear Schrödinger equation	1
The Bessel kernel determinant on large intervals and Birkhoff's ergodic theorem	1
Landscape complexity beyond invariance and the elastic manifold	1
Large deviations principle for the cubic NLS equation	1
Compressive phase retrieval: Optimal sample complexity with deep generative priors	1
Arnold diffusion in Hamiltonian systems on infinite lattices	1
Free Energy Wells and Overlap Gap Property in Sparse PCA	1
Prescribed curvature measure problem in hyperbolic space	1
Quantitative homogenization of principal Dirichlet eigenvalue shape optimizers	1
A Relative Entropy and a Unique Continuation Result for Ricci Expanders	1
Sigma Delta Quantization for Images	1
An Extremal Problem Arising in the Dynamics of Two‐Phase Materials That Directly Reveals Information about the Internal Geometry	1