#  Colloquium Series: Mehtaab Sawhney 

 



####  calendar\_today Date and Time 

 **October 20, 2025** 

 12:00PM - 01:00PM EDT 

####  pin\_drop Location 

 **Science Center, Room 316**  



 

 



 

Our upcoming event for the Statistics Colloquium Series is scheduled for Monday, October 20 from 12:00 – 1:00pm (ET) and will be an in-person presentation Science Center 316. Lunch will be provided to guests following the talk. This week's speaker will be Mehtaab Sawhney, assistant professor at Columbia University's Mathematics Department.

**Hitting time mixing for the transposition walk**

Consider shuffling a deck of n cards, labeled 1 through n, as follows: at each time step, pick one card uniformly with your right hand and another card, independently and uniformly with your left hand; then swap the cards. How long does it take until the deck is close to random?  
  
Confirming a conjecture of N. Berestycki, we prove the definitive "hitting time" version for the mixing of this shuffle. Let τ denote the first time at which all cards have been touched. The total variation distance between the stopped distribution at τ and the uniform distribution on permutations is o\_n(1); this is best possible, since at time τ−1, the total variation distance is at least (1+o\_n(1))/e. A key feature of this proof is to combine the representation theoretic inputs of Diaconis and Shahshahani with a physical space argument.  
Based on joint work w. Vishesh Jain

Mehtaab Sawhney is a Clay Research Fellow and a tenure-track assistant professor at Columbia University. His research interests are broadly within combinatorics, probability, analytic number theory and theoretical computer science.



 

 



 

 

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