Welcome! I am a researcher at the Broad Institute of MIT and Harvard, where I am supervised by Caroline Uhler. I recently (May 2020) finished my NSF RTG postdoc at the University of Michigan Statistics Department where my supervisor was Elizaveta Levina. Prior to this I obtained my PhD on June 2017 at the MIT Mathematics Department where I was advised by Alice Guionnet. Before doing my PhD, I graduated in 2012 from UC Davis with a Bachelors degree in Mathematics and Physics. For the academic year of 2020–2021 I was unable to start a position abroad (outside of the United States) due to COVID. I am interested in probability theory and its applications to problems in statistics.

Most of my research has been in the area of random matrices and a few related fields. In many of my papers I study the behavior of linear statistics of eigenvalues. Lately, I've been thinking about causal inference and its applications to biology and medical research. Below are a list of my publications and preprints.

**Publications**- [Journal] “Covariance Kernel of Linear Spectral Statistics for Half-Heavy tailed Wigner Matrices.” Asad Lodhia and Anna Maltsev. Random Matrices: Theory and Applications, Volume 12, no. 2, 2250054 (2023).
- [Journal] “Harmonic Means of Wishart Random Matrices.” Asad Lodhia. Random Matrices: Theory and Applications, Volume 10, no. 2, 2150016 (2021).
- [Journal] “Marčenko-Pastur Law for Kendall's Tau.” Afonso Bandeira, Asad Lodhia and Philippe Rigollet. Electronic Communications in Probability, Volume 22 (2017), no. 32, 1–7.
- [Journal] “Mesoscopic Central Limit Theorem for general β-ensembles.” Florent Bekerman and Asad Lodhia. Ann. Inst. H. Poincaré Prob. Stat. Volume 54, Number 4 (2018), 1917–1938.
- [Journal] “Fractional Gaussian fields: a survey.” Asad Lodhia, Scott Sheffield, Xin Sun and Samuel Watson. Probability Surveys, Vol. 13, 1–56.
**Preprints**- [arXiv] “Mesoscopic linear statistics of Wigner Matrices.” Asad Lodhia and Nick Simm. Posted 2015.

**Publications**- [Journal] “Matrix Means and a Novel High-Dimensional Shrinkage Phenomenon.” Asad Lodhia, Keith Levin and Elizaveta Levina. Bernoulli 28(4): 2578-2605 (November 2022).
- [Journal] “Phase Transitions in the Dynamic Mode Decomposition.” Arvind Prasadan, Asad Lodhia and Raj Rao Nadakuditi. 2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2019, pp. 396–400.
- [Journal] “Recovering low-rank structure from multiple networks with unknown edge distributions.” Keith Levin, Asad Lodhia, and Elizaveta Levina. Journal of Machine Learning Research, Volume 23 (2022), no. 3, pp. 1–48.

**Preprints**- [arXiv] “Positivity in Linear Gaussian Structural Equation Models” Asad Lodhia, Jan-Christian Hutter, Caroline Uhler, and Piotr Zwiernik. Posted May 2023.

I've reviewed papers for Annals of Statistics, Bernoulli, the Journal of Random Matrix Theory and Applications, IEEE transactions and COLT.

Below are some links to other websites with information about my research.

We may have met before in a conference or summer school! If so feel free to send me an email if you want to catch up, or touch base, or get notes, or ask a question, etc… If you're not sure if we've met, or if my name sounds familiar, or maybe you're just curious, etc… I've listed some conferences I've attended (or plan on attending) below.

**2023**- June: Invited talk at MD Anderson Department of Biostatistics

Below are a list of classes I have taught at the University of Michigan. If you are a past student and need a letter of recommendation feel free to request one. Depending on the letter requested (graduate school application, job application, etc…) I would appreciate an appropriate amount of time to write the letter. I can write a better letter for you if we've had interactions in or out of class, or if you've distinguished yourself in some way.

I have experience doing directed readings with undergraduates from my time in graduate school where I participated three times in the MIT Mathematics Directed Reading program and during my postdoc at Michigan where I organized a Reinforcement Learning directed reading group.

**Winter 2020:**- Statistics 430: Topics in Applied Probability.
**Fall 2019:**- Statistics 510: Introduction to Probability Theory.
**Winter 2019:**- Statistics 430: Topics in Applied Probability.
**Fall 2018:**- Statistics 510 - Introduction to Probability Theory.
**Winter 2018:**- Statistics 430 - Topics in Applied Probability.
**Fall 2017:**- Statistics 510 - Introduction to Probability Theory.

My email is

asaddotidotlodhiaatgmail.com