Stéphane Boucheron contributed, with Gábor Lugosi and Pascal Massart, to the concentration theory of self-bounding functions. Their paper turns coordinatewise increment bounds into exponential tail bounds through the entropy method (probability). This supplies a reusable route from a function's local sensitivity to global concentration of measure.^[ref]

Gábor Lugosi coauthored concentration inequalities for self-bounding functions with Stéphane Boucheron and Pascal Massart. Their analysis uses the entropy method (probability) and a refined Herbst argument. Small coordinatewise changes can therefore yield strong control of a function's fluctuations even when it depends on many independent inputs.^[ref]

Pascal Massart coauthored concentration bounds for self-bounding functions with Stéphane Boucheron and Gábor Lugosi. Their entropy method (probability) analysis derives Bernstein-type concentration inequalities from restrictions on how much one coordinate can change a function. The work also recovers Talagrand's convex distance inequality.^[ref]

J. Ginibre coauthored the FKG inequality with C. M. Fortuin and P. W. Kasteleyn. They proved positive correlation of increasing functions on a finite distributive lattice under a condition on its probability weights, with applications to Ising models and the random-cluster model.^[ref]

Ashok K. Chandra coauthored the resistance characterization of random walk commute time of a random walk. The identity $H_{st}+H_{ts}=2m{R}_{st}$ relates expected travel times on a graph to effective resistance in its unit-resistor network.^[ref]

Prabhakar Raghavan coauthored an electrical-network method for studying random walks. Their exact commute time of a random walk identity and resistance bounds on cover time connect the geometry of a graph with the time required to explore it.^[ref]

Walter L. Ruzzo coauthored bounds linking random walk cover time to electrical-network resistance. The paper also proves the exact commute time of a random walk identity, enabling deterministic effective resistance calculations to control expected exploration times.^[ref]

Roman Smolensky contributed to the electrical-network analysis of random walks on graphs. The joint work identifies commute time of a random walk with $2mR$, translating a stochastic round trip into an effective resistance calculation.^[ref]

Prasoon Tiwari coauthored the connection between effective resistance and random walk times. For an undirected graph with $m$ unit-resistance edges, the commute time of a random walk between two vertices equals $2m$ times their effective resistance.^[ref]

Art B. Owen developed and presented empirical likelihood, a form of nonparametric statistics that assigns probabilities to observed data points instead of selecting a parametric family. His monograph explains how likelihood constraints can encode a proposed population mean or other parameter. This preserves likelihood-based inference while avoiding a fixed parametric shape for the underlying probability distribution.^[ref]

Sabyasachi Chatterjee coauthored improved risk bounds for isotonic regression with Adityanand Guntuboyina and Bodhisattva Sen. The monotone least-squares estimator achieves a range of rates depending on the underlying sequence, including nearly parametric behavior for constant signals. Their local minimax analysis explains why more rapidly varying monotone signals are intrinsically harder to estimate.^[ref]

Adityanand Guntuboyina contributed to risk bounds for isotonic regression with Sabyasachi Chatterjee and Bodhisattva Sen. They quantified how the error of the monotone least-squares estimator depends on the shape of the true sequence. Nearly flat signals permit faster estimation than uniformly increasing signals, an example of adaptation to structure without specifying that structure in advance.^[ref]

Bodhisattva Sen coauthored improved risk bounds for isotonic regression with Sabyasachi Chatterjee and Adityanand Guntuboyina. Their analysis shows that the least-squares estimator adapts to the number of constant pieces of a monotone signal. The work also provides local minimax lower bounds, helping distinguish an estimator's limitations from limitations inherent in the data.^[ref]

Ismaël Castillo studied nonparametric Bernstein-von Mises theorems with Richard Nickl. In the Gaussian white noise model, they constructed Bayesian credible sets with asymptotically exact frequentist coverage under stated assumptions. Their analysis also treats functionals, illustrating how an infinite-dimensional unknown function can still yield well-calibrated inference for particular observable quantities.^[ref]

Richard Nickl coauthored nonparametric Bernstein-von Mises theorems with Ismaël Castillo for the Gaussian white noise model. Their work explains when Bayesian credible sets can also have asymptotically correct frequentist coverage probability. The result connects the limiting posterior geometry with efficient inference on an unknown function, rather than only a fixed finite-dimensional parameter.^[ref]

Matthias Heymann coauthored the geometric minimum action with Eric Vanden-Eijnden. Their algorithm minimizes a geometric form of the Freidlin--Wentzell action to calculate rare transition paths and the quasipotential. Examples include a bistable stochastic differential equation and a genetic-switch Markov jump process, showing how one variational principle applies to different stochastic models.^[ref]

Eric Vanden-Eijnden developed the geometric minimum action with Matthias Heymann. The method computes likely transition paths between states exhibiting metastability in weakly noisy dynamical systems. Reformulating the Freidlin--Wentzell action on curves removes an unnecessary dependence on the speed at which a candidate path is traversed, making the free-time optimization more tractable.^[ref]

Sharad Goel coauthored a method for estimating mixing time of a Markov chain through the spectral profile, with Ravi Montenegro and Prasad Tetali. Their analysis gives upper and lower convergence bounds and applies them to several families of graphs. The central mechanism is to track how relaxation changes with the stationary mass of a function's support.^[ref]

Ravi Montenegro contributed, with Sharad Goel and Prasad Tetali, to bounds on mixing time of a Markov chain using the spectral profile. Their approach adapts Faber-Krahn inequalities to finite Markov chains and compares the resulting bounds with conductance of a Markov chain methods. It captures information at multiple set sizes that a single bottleneck estimate can miss.^[ref]

Prasad Tetali coauthored the spectral profile method for bounding mixing time of a Markov chain with Sharad Goel and Ravi Montenegro. It refines a single spectral gap by considering functions supported on sets of different stationary masses. This makes the geometry of small sets useful for quantifying convergence to the stationary distribution.^[ref]