Probability & Statistics
Research in probability and mathematical statistics spans from foundational measure-theoretic probability through stochastic analysis and random structures to the statistical theory underpinning modern data science. Key contemporary themes include stochastic partial differential equations, random matrix theory, high-dimensional statistics, and the probabilistic methods that power machine-learning theory.
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math.PR Probability
Probability theory, stochastic processes, stochastic analysis, random structures.
math.ST Statistics Theory
Mathematical statistics, asymptotics, decision theory, nonparametric methods.
stat.TH Statistics: Theory
Statistical theory as indexed by the statistics category of arXiv.
Active research areas
The most active problem clusters right now.
Random matrix theory
Universality, local laws, connections to number theory (Riemann zeros), free probability.
Search arXiv →SLE and conformal invariance
Schramm-Loewner evolution, critical lattice models, conformal field theory.
Search arXiv →Stochastic PDEs
KPZ equation, Φ⁴ models, regularity structures (Hairer), paracontrolled distributions.
Search arXiv →High-dimensional statistics
Compressed sensing, random projections, estimation under sparsity, minimax theory.
Search arXiv →Statistical learning theory
Concentration inequalities, PAC-Bayes, generalization bounds, theory of neural networks.
Search arXiv →Landmark results
Major results shaping the field.
- 2000
Schramm-Loewner evolution
Conformal-invariant description of critical 2D lattice models (Werner Fields Medal 2006).
- 2010
Tao–Vu on random matrices
Four-moment theorem establishing universality.
- 2013
Hairer on KPZ
Solution to the Kardar-Parisi-Zhang equation via regularity structures.
- ongoing
Tsybakov-led minimax theory
Rates of convergence for nonparametric problems in high dimensions.
Leading journals
Where current research in this area is published.