52 citations · 116 across the 22 of their papers we have counts for
26 papers
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 $…
Nodal Count for Orthogonally Invariant Ensembles
Lior Alon, Dan Mikulincer, John Urschel
We investigate the nodal count of eigenvectors of random matrices interpreted as operators on signed complete graphs. Our focus is on orthogonally invariant ensembles, with particu…
Low-dimensional Functions are Efficiently Learnable under Randomly Biased Distributions
Elisabetta Cornacchia, Dan Mikulincer, Elchanan Mossel
The problem of learning single index and multi index models has gained significant interest as a fundamental task in high-dimensional statistics. Many recent works have analysed gr…
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…
Time Lower Bounds for the Metropolis Process and Simulated Annealing
Zongchen Chen, Dan Mikulincer, Daniel Reichman +1
The Metropolis process (MP) and Simulated Annealing (SA) are stochastic local search heuristics that are often used in solving combinatorial optimization problems. Despite signific…
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…
Is this correct? Let's check!
Omri Ben-Eliezer, Dan Mikulincer, Elchanan Mossel +1
Societal accumulation of knowledge is a complex process. The correctness of new units of knowledge depends not only on the correctness of new reasoning, but also on the correctness…
Archimedes Meets Privacy: On Privately Estimating Quantiles in High Dimensions Under Minimal Assumptions
Omri Ben-Eliezer, Dan Mikulincer, Ilias Zadik
The last few years have seen a surge of work on high dimensional statistics under privacy constraints, mostly following two main lines of work: the ``worst case'' line, which does…
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…
Size and depth of monotone neural networks: interpolation and approximation
Dan Mikulincer, Daniel Reichman
We study monotone neural networks with threshold gates where all the weights (other than the biases) are non-negative. We focus on the expressive power and efficiency of representa…
Integrality Gaps for Random Integer Programs via Discrepancy
Sander Borst, Daniel Dadush, Dan Mikulincer
We prove new bounds on the additive gap between the value of a random integer program with constraints and that of its linear programming…
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…
Community detection and percolation of information in a geometric setting
Ronen Eldan, Dan Mikulincer, Hester Pieters
We make the first steps towards generalizing the theory of stochastic block models, in the sparse regime, towards a model where the discrete community structure is replaced by an u…
Network size and weights size for memorization with two-layers neural networks
Sébastien Bubeck, Ronen Eldan, Yin Tat Lee +1
In 1988, Eric B. Baum showed that two-layers neural networks with threshold activation function can perfectly memorize the binary labels of points in general position in $\math…
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_…
How to trap a gradient flow
Sébastien Bubeck, Dan Mikulincer
We consider the problem of finding an -approximate stationary point of a smooth function on a compact domain of . In contrast with dimension-free approac…
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…
Stability of the Shannon-Stam inequality via the Föllmer process
Ronen Eldan, Dan Mikulincer
We prove stability estimates for the Shannon-Stam inequality (also known as the entropy-power inequality) for log-concave random vectors in terms of entropy and transportation dist…