John Pike

Office: DMF 435
Email: john DOT pike AT bridgew DOT edu
Mailing Address:
Mathematics Department
Dana Mohler-Faria Science & Mathematics Center, Room 431
24 Park Avenue
Bridgewater, MA 02325

General

I am currently an associate professor at Bridgewater State University. Before coming to BSU, I was a postdoc at Cornell University, and before that I was at the University of Southern California where I received my PhD under the direction of Jason Fulman.

Additional information can be found in my CV.

Teaching

For the Fall 2024 semester, I am teaching Math 180 (Transition to Advanced Math), Math 202 (Linear Algebra), Math 401 (Real Analysis), and Math 403 (Probability).

Research

My research is primarily concerned with probability theory and its applications. I am particularly interested in Markov chains defined on algebraic and combinatorial structures and in distributional approximation using Stein's method techniques.

Feel free to check out these papers for further details:

• Double jump phase transition in a soliton cellular automaton, with Lionel Levine and Hanbaek Lyu, Int. Math. Res. Not. IMRN 2022, no. 1.
   
• Positional voting and doubly stochastic matrices, with Jacqueline Anderson and Brian Camara, Amer. Math. Monthly 128 (2021), no. 4.
   
• Mixing time and eigenvalues of the abelian sandpile Markov chain, with Daniel Jerison and Lionel Levine, Trans. Amer. Math. Soc.372 (2019), no. 12.
   
• Poisson statistics of eigenvalues in the hierarchical Dyson model, with Alexander Bendikov and Anton Braverman, Theory Probab. Appl. 63 (2018), no. 1.
  Russian translation: Teor. Veroyatnost. i Primenen., 63 (2018), no. 1.
   
• Stein's method and the Laplace distribution, with Haining Ren, ALEA Lat. Am. J. Probab. Math. Stat. 11 (2014), no. 1.
   
• Eigenfunctions for random walks on hyperplane arrangements, Ph.D. Thesis, University of Southern California (2013).
   
• A note on the Poincaré and Cheeger inequalities for simple random walk on a connected graph, arXiv note (2012).
   
• Convergence rates for generalized descents, Electron. J. Combin. 18 (2011), no. 1.

Probability Notes

You are also welcome to look at my old notes for Basic Probability, Probability Theory I, Probability Theory II, and Random Walks & Representations.

Algebraic aspects of the latter are developed more fully in these notes on Representations of Finite Groups.