52 citations · 116 across the 22 of their papers we have counts for
14 papers · 1 filter
Marchenko-Pastur law for tensor powers of exchangeable unconditional vectors
Feng Cheng, Dan Mikulincer
Given an isotropic, exchangeable, and unconditional random vector , we consider the sample covariance matrix constructed from i.i.d. copies of several tensor models of $…
Stochastic Localization with Non-Gaussian Tilts and Applications to Tensor Ising Models
Dan Mikulincer, Arianna Piana
We present generalizations and modifications of Eldan's Stochastic Localization process, extending it to incorporate non-Gaussian tilts, making it useful for a broader class of mea…
Stochastic proof of the sharp symmetrized Talagrand inequality
Thomas A. Courtade, Max Fathi, Dan Mikulincer
We give a new proof of the sharp symmetrized form of Talagrand's transport-entropy inequality. Compared to stochastic proofs of other Gaussian functional inequalities, the new idea…
Characterizing the fourth-moment phenomenon of monochromatic subgraph counts via influences
Nitya Mani, Dan Mikulincer
We investigate the distribution of monochromatic subgraph counts in random vertex -colorings of large graphs. We give sufficient conditions for the asymptotic normality of these…
Transportation onto log-Lipschitz perturbations
Max Fathi, Dan Mikulincer, Yair Shenfeld
We establish sufficient conditions for the existence of globally Lipschitz transport maps between probability measures and their log-Lipschitz perturbations, with dimension-free bo…
Noise stability on the Boolean hypercube via a renormalized Brownian motion
Ronen Eldan, Dan Mikulincer, Prasad Raghavendra
We consider a variant of the classical notion of noise on the Boolean hypercube which gives rise to a new approach to inequalities regarding noise stability. We use this approach t…
On the Lipschitz properties of transportation along heat flows
Dan Mikulincer, Yair Shenfeld
We prove new Lipschitz properties for transport maps along heat flows, constructed by Kim and Milman. For (semi)-log-concave measures and Gaussian mixtures, our bounds have several…
The Brownian transport map
Dan Mikulincer, Yair Shenfeld
Contraction properties of transport maps between probability measures play an important role in the theory of functional inequalities. The actual construction of such maps, however…
Anti-concentration of polynomials: dimension-free covariance bounds and decay of Fourier coefficients
Itay Glazer, Dan Mikulincer
We study random variables of the form , when is a degree polynomial, and is a random vector on , motivated towards a deeper understanding of the c…
Non-asymptotic approximations of neural networks by Gaussian processes
Ronen Eldan, Dan Mikulincer, Tselil Schramm
We study the extent to which wide neural networks may be approximated by Gaussian processes when initialized with random weights. It is a well-established fact that as the width of…
Stability estimates for invariant measures of diffusion processes, with applications to stability of moment measures and Stein kernels
Max Fathi, Dan Mikulincer
We investigate stability of invariant measures of diffusion processes with respect to distances on the coefficients, under an assumption of log-concavity. The method is a var…
A CLT in Stein's distance for generalized Wishart matrices and higher order tensors
Dan Mikulincer
We study the central limit theorem for sums of independent tensor powers, . We focus on the high-dimensional regime where $X_…
Stability of Talagrand's Gaussian transport-entropy inequality via the Föllmer process
Dan Mikulincer
We establish a dimension-free improvement of Talagrand's Gaussian transport-entropy inequality, under the assumption that the measures satisfy a Poincaré inequality. We also study…
The CLT in high dimensions: quantitative bounds via martingale embedding
Ronen Eldan, Dan Mikulincer, Alex Zhai
We introduce a new method for obtaining quantitative convergence rates for the central limit theorem (CLT) in a high dimensional setting. Using our method, we obtain several new bo…