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I am an Instructor (postdoc) at MIT Mathematics.
Prior to that I finished my Ph.D. at the Weizmann Institute, Faculty of Mathematics, where I was advised by Ronen Eldan.
Before coming to Weizmann, I completed my B.Sc. in Mathematics and Computer Science at Ben-Gurion University (BGU), where I also studied Cognitive Neuroscience.
I've spent the summer of 2019 at Microsoft Research AI, hosted by Sébastien Bubeck.
I am also an Azrieli fellow.

My research interests broadly lie at the union of high-dimensional geometry, probability, statistics, information theory, and their relation to data science and learning theory. I am particularly interested in normal approximations and dimension-free phenomena.

Email: danmiku (at) gmail (dot) com

• Time Lower Bounds for the Metropolis Process and Simulated Annealing,
  Zongchen Chen, Dan Mikulincer, Daniel Reichman and Alex Wein,
  preprint (2023). [arXiv]


• Transportation onto log-Lipschitz perturbations,
  Max Fathi, Dan Mikulincer and Yair Shenfeld,
  Calculus of Variations and Partial Differential Equations, to appear (2023). [arXiv][slides]


• Is this correct? Let's check!,
  Omri Ben-Eliezer, Dan Mikulincer, Elchanan Mossel and Madhu Sudan,
  ITCS 2023. [arXiv][talk]


• Archimedes meets privacy: on privately estimating quantiles in high dimensions under minimal assumptions,
  Omri Ben-Eliezer, Dan Mikulincer and Ilias Zadik,
  NeurIPS 2022. [arXiv]


• Noise stability on the Boolean hypercube via a renormalized Brownian motion,
  Ronen Eldan, Dan Mikulincer and Prasad Raghavendra,
  STOC 2023. [arXiv][slides][talk]


• Size and depth of monotone neural networks: interpolation and approximation,
  Dan Mikulincer and Daniel Reichman,
  NeurIPS 2022. [arXiv]


• Integrality gaps for random integer programs via discrepancy,
  Sander Borst, Daniel Dadush and Dan Mikulincer,
  SODA 2023. [arXiv]


• On the Lipschitz properties of transportation along heat flows,
  Dan Mikulincer and Yair Shenfeld,
  GAFA Seminar Notes (2022). [arXiv][slides]


• The Brownian transport map,
  Dan Mikulincer and Yair Shenfeld,
  Preprint (2021). [arXiv][slides][talk]


• Anti-concentration of polynomials: dimension-free covariance bounds and decay of Fourier coefficients,
  Itay Glazer and Dan Mikulincer,
  Journal of Functional Analysis (2021). [arXiv][slides]


• Non-asymptotic approximations of neural networks by Gaussian processes,
  Ronen Eldan, Dan Mikulincer and Tselil Schramm,
  COLT 2021. [arXiv][slides][talk][poster]


• Stability estimates for invariant measures of diffusion processes, with applications to stability of moment measures and Stein kernels,
  Max Fathi and Dan Mikulincer,
  The Annali della Scuola Normale Superiore di Pisa (2020). [arXiv][slides][talk]


• Community detection and percolation of information in a geometric setting,
  Ronen Eldan, Dan Mikulincer and Hester Pieters,
  Combinatorics, Probability and Computing (2020). [arXiv]


• Network size and weights size for memorization with two-layers neural networks,
  Sébastien Bubeck, Ronen Eldan, Yin Tat Lee and Dan Mikulincer,
  NeurIPS 2020. [arXiv][slides][talk]


• A CLT in Stein's distance for generalized Wishart matrices and higher order tensors,
  Dan Mikulincer,
  International Mathematics Research Notices (2020). [arXiv][slides][talk]


• How to trap a gradient flow,
  Sébastien Bubeck and Dan Mikulincer,
  COLT 2020. [arXiv][slides][talk]


• Stability of Talagrand's Gaussian transport-entropy inequality via the Föllmer process,
  Dan Mikulincer,
  Israel Journal or Mathematics (2020). [arXiv][slides]


• Stability of the Shannon-Stam inequality via the Föllmer process,
  Ronen Eldan and Dan Mikulincer,
  Probability Theory and Related Fields (2020). [arXiv][slides]


• The CLT in high dimensions: quantitative bounds via martingale embedding,
  Ronen Eldan, Dan Mikulincer and Alex Zhai,
  Annals of Probability (2020). [arXiv][slides]


• Information and dimensionality of anisotropic random geometric graphs,
  Ronen Eldan and Dan Mikulincer,
  GAFA Seminar Notes (2019). [arXiv][poster]



Papers in quantitative Neurobiology

• Monitoring and quantifying dynamic physiological processes in live neurons using fluorescence recovery after photobleaching,
  Kevin Staras, Dan Mikulincer and Daniel Gitler,
  Journal of Neurochemistry, Volume 126, Issue 2, Pages 213-222 (2013).


• ATP binding to synaspsin IIa regulates usage and clustering of vesicles in terminals of hippocampal neurons,
  Yoav Shulman, Alexandra Stavsky, Tatiana Fedorova, Dan Mikulincer, Merav Atias, Igal Radinsky, Joy Kahn, Inna Slutsky and Daniel Gitler,
  Journal of Neuroscience, Volume 35, Issue 3, Pages 985-998 (2015).