About

Sourav Chatterjee is a Professor of Mathematics and Statistics at Stanford University, USA. His research interests include probability theory, statistics, and mathematical physics, with a focus on topics such as Liouville field theory, spin glasses, and large deviations in random graphs.

Research topics

• Demographic economics
• Economics
• Economic growth

Selected publications

• Transforming Primary Education through Artificial Intelligence: Policy Vision and Pedagogical Challenges in India

  International Journal of Research and Review · 2026-03-24

  articleOpen access1st authorCorresponding

  Artificial Intelligence (AI) is simply transforming the world, in all aspects, including economies, society and how we learn, and this change is very relatable even in a college context. Even though universities still rely on higher education, they are seeing that as nations strive to more future-oriented schooling systems, exposure to artificial intelligence concepts, earlier in life, is becoming more important in shaping younger generations in our more digital, automated world. As a way of discussing why we need to introduce AI in the primary school curriculum of India, the paper relies on the National Education Policy (NEP) 2020 and the National Curriculum Framework of School Education (NCF-SE) 2023 as the frameworks to discuss the issue. It also examines the pedagogical advantages, structural barrier, ethical issues, and implementation plans of responsible, inclusive, and context-specific AI learning utilizing a policy-analysis approach. In a nutshell, it can be argued that AI, under the priorities of core learning and equity-oriented pedagogy, can transform classroom practice, enhance individualized learning, and equip students with early practical AI skills and critical ethical judgment. This study focuses on the view of teacher educators regarding the incorporation of artificial intelligence in primary education with a spotlight on pedagogical readiness, ethical accountability, and professional metamorphosis. It claims that successful AI integration mainly hinges on developmentally suitable teacher education that goes hand in hand with the National Education Policy 2020 and the National Curriculum Framework for School Education 2023, thus making sure that the use of technology is to enable, and not replace, human, centered pedagogy. The research brings out that there is a need of critical AI literacy, AI implementation concentrating on fairness, and continuous professional development to enable teachers to be not only reflective but also ethically grounded practitioners of AI, supported classrooms. Keywords: Artificial Intelligence, economies, society, NEP 2020, inclusive, accountability, professional metamorphosis

  PublisherDOI

• Neural networks generalize on low complexity data

  The Annals of Statistics · 2026-02-01

  article1st authorCorresponding

  We show that feedforward neural networks with ReLU activation generalize on low complexity data, suitably defined. Given i.i.d. data generated from a simple programming language, the minimum description length (MDL) feedforward neural network which interpolates the data generalizes with high probability. We define this simple programming language, along with a notion of description length of such networks. We provide several examples on basic computational tasks, such as checking primality of a natural number. For primality testing, our theorem shows the following and more. Suppose that we draw an i.i.d. sample of n numbers uniformly at random from 1 to N. For each number xi, let yi=1 if xi is a prime and 0 if it is not. Then the interpolating MDL network accurately answers, with probability 1−O((lnN)/n), whether a newly drawn number between 1 and N is a prime or not. Note that the network is not designed to detect primes; minimum description learning discovers a network which does so. Extensions to noisy data are also discussed, suggesting that MDL neural network interpolators can demonstrate tempered overfitting.

  PublisherDOI

• Rigorous results for timelike liouville field theory

  Forum of Mathematics Sigma · 2026-01-01

  articleOpen access1st authorCorresponding

  Abstract Liouville field theory has long been a cornerstone of two-dimensional quantum field theory and quantum gravity, which has attracted much recent attention in the mathematics literature. Timelike Liouville field theory is a version of Liouville field theory where the kinetic term in the action appears with a negative sign, which makes it closer to a theory of quantum gravity than ordinary (spacelike) Liouville field theory. Making sense of this “wrong sign” requires a theory of Gaussian random variables with negative variance. Such a theory is developed in this paper, and is used to prove the timelike DOZZ formula for the $3$ -point correlation function when the parameters satisfy the so-called “charge neutrality condition.” Expressions are derived also for the k -point correlation functions for all $k\ge 3$ , and it is shown that these functions approach the correct semiclassical limits as the coupling constant is sent to zero.

  PublisherOA PDFDOI

• A scaling limit of SU(2) lattice Yang–Mills–Higgstheory

  Probability and Mathematical Physics · 2026-05-18

  preprintOpen access1st authorCorresponding

  The construction of non-Abelian Euclidean Yang-Mills theories in dimension four, as scaling limits of lattice Yang-Mills theories or otherwise, is a central open question of mathematical physics. This paper takes the following small step towards this goal. In any dimension $d\ge 2$, we construct a scaling limit of $\mathrm{SU}(2)$ lattice Yang-Mills theory coupled to a Higgs field (under the degenerate potential) transforming in the fundamental representation of $\mathrm{SU}(2)$. After unitary gauge fixing and taking the lattice spacing $\varepsilon\to 0$, and simultaneously taking the gauge coupling constant $g\to 0$ and the Higgs length $α\to \infty$ in such a manner that $αg$ is always equal to $c\varepsilon$ for some fixed $c$ and $g= O(\varepsilon^{50d})$, a stereographic projection of the gauge field is shown to converge to a massive Gaussian field. This gives the first construction of a scaling limit of a non-Abelian lattice Yang-Mills theory in a dimension higher than two, as well as the first rigorous proof of mass generation by the Higgs mechanism in such a theory. Analogous results are proved for $\mathrm{U}(1)$ theory as well. The question of constructing a non-Gaussian scaling limit remains open.

  PublisherDOI

• Permuton and local limits for the Luce model

  ArXiv.org · 2025-09-09

  preprintOpen access

  We investigate the asymptotic properties of permutations drawn from the Luce model, a natural probabilistic framework in which permutations are generated sequentially by sampling without replacement, with selection probabilities proportional to prescribed positive weights. These permutations arise in applications such as ranking models, the Tsetlin library, and related Markov processes. Under minimal assumptions on the weights, we establish a permuton limit theorem describing the global behavior of Luce-distributed permutations and derive an explicit density of the limiting permuton. We further compute limiting pattern densities and analyze the differences between exact Luce permutations and their permuton approximations. We also study the local convergence of these permutations, proving a quenched Benjamini--Schramm limit and a central limit theorem for consecutive pattern occurrences. Finally, we prove a central limit theorem for the number of inversions.

  PublisherOA PDFDOI

• Spectral gap of nonreversible Markov chains

  The Annals of Applied Probability · 2025-08-01 · 2 citations

  article1st authorCorresponding
  PublisherDOI

• Correlation decay for U(1) lattice Higgs theory: the case of small mass

  ArXiv.org · 2025-09-23

  preprintOpen access1st authorCorresponding

  We study the lattice Yang-Mills-Higgs model with inverse gauge coupling $β>0$ and Higgs length $α>0$, in the ``complete breakdown of symmetry" regime. For lattice dimension $d\ge 2$ and (abelian) gauge group U(1), we prove that for any $m>0$, if $α= mβ$ and $β$ is large enough, the model exhibits exponential decay of correlations. This extends the classical result of Osterwalder and Seiler (1978), who required in addition that $m$ be sufficiently large. Our result also verifies a phase diagram from the physics literature, predicted by Fradkin and Shenker (1979). The proof is based on the Glimm-Jaffe-Spencer cluster expansion around a massive Gaussian field, following the approach of Balaban et al. (1984).

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• Effect of Magneto-Mechanical Synergism in the Process-Structure Correlation in Fe-C Alloys: A Phase-Field Modeling Approach

  ArXiv.org · 2025-11-26

  preprintOpen access

  Applied magnetic fields can alter phase equilibria and kinetics in steels; however, quantitatively resolving how magnetic, chemical, and elastic driving forces jointly influence the microstructure remains challenging. We develop a quantitative magneto-mechanically coupled phase-field model for the Fe-C system that couples a CALPHAD-based chemical free energy with demagnetization-field magnetostatics and microelasticity. The model reproduces single- and multi-particle evolution during the alpha to gamma inverse transformation at 1023 K under external fields up to 20 T, including ellipsoidal morphologies observed experimentally at 8 T. Chemically driven growth is isotropic; a magnetic interaction introduces an anisotropic driving force that elongates gamma precipitates along the field into ellipsoids, while elastic coherency promotes faceting, yielding elongated cuboidal or ``brick-like" particles under combined magneto-elastic coupling. Growth kinetics increase with C content, and decrease with field strength and misfit strain. Multi-particle simulations reveal dipolar interaction-mediated coalescence for field-parallel neighbors and ripening for field-perpendicular neighbors. Incorporating field-dependent diffusivity from experiment slows kinetics as expected; a first-principles-motivated anisotropic diffusivity correction is estimated to be small (<2%). These results establish a process-structure link for magnetically assisted heat treatments of Fe-C alloys and provide guidance for microstructure control via chemo-magneto-mechanical synergism.

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• Estimating the size of a set using cascading exclusion

  ArXiv.org · 2025-08-07

  preprintOpen access1st authorCorresponding

  Let $S$ be a finite set, and $X_1,\ldots,X_n$ an i.i.d. uniform sample from $S$. To estimate the size $|S|$, without further structure, one can wait for repeats and use the birthday problem. This requires a sample size of the order $|S|^\frac{1}{2}$. On the other hand, if $S=\{1,2,\ldots,|S|\}$, the maximum of the sample blown up by $n/(n-1)$ gives an efficient estimator based on any growing sample size. This paper gives refinements that interpolate between these extremes. A general non-asymptotic theory is developed. This includes estimating the volume of a compact convex set, the unseen species problem, and a host of testing problems that follow from the question `Is this new observation a typical pick from a large prespecified population?' We also treat regression style predictors. A general theorem gives non-parametric finite $n$ error bounds in all cases.

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• Univariate-Guided Sparse Regression

  Harvard Data Science Review · 2025-07-18

  article1st authorCorresponding
  PublisherDOI

Recent grants

• Concentration of measure, large deviations, normal approximation and applications

  NSF · $310k · 2013–2017

• Mathematical Foundations for Yang-Mills Theory, Randomly Growing Surfaces, and Related Systems

  NSF · $330k · 2022–2025

• Normal Approximation, Fair Allocations, Interacting Brownian Particles, and Applications

  NSF · $130k · 2007–2010

• Two-Dimensional KPZ Evolution, Fluctuation Lower Bounds, and Ultrametricity

  NSF · $300k · 2019–2022

• Lattice Gauge Theories, Importance Sampling, and Quantum Unique Ergodicity

  NSF · $300k · 2016–2019

Frequent coauthors

• Persi Diaconis

  40 shared

• Qi-Man Shao

  17 shared

• Allan Sly

  Princeton University

  12 shared

• S. R. S. Varadhan

  12 shared

• Amir Dembo

  Stanford University

  10 shared

• Laurent Miclo

  Institut de Mathématiques de Toulouse

  9 shared

• Erik Bates

  9 shared

• Michel Ledoux

  6 shared

Awards & honors

• Elected to AAAS (American Academy of Arts & Sciences)
• Royal Society Fellow