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Fluctuation results for size of the vacant set for random walks on discrete torus
Partha Dey, Daesung Kim
We consider one or more independent random walks on the dimensional discrete torus. The walks start from vertices chosen independently and uniformly at random. We analyze…
A note on Stein equation for weighted sums of independent distributions
Xiaohui Chen, Partha Dey
This note provides the Stein equation for weighted sums of independent distributions.
Longest increasing path within the critical strip
Partha Dey, Mathew Joseph, Ron Peled
A Poisson point process of unit intensity is placed in the square . An increasing path is a curve connecting with which is non-decreasing in each coordinat…
On Normalized Multiplicative Cascades under Strong Disorder
Partha S. Dey, Edward Waymire
Multiplicative cascades, under weak or strong disorder, refer to sequences of positive random measures , parameterized by a positive disorder parameter ,…
High temperature limits for -dimensional directed polymer with heavy-tailed disorder
Partha S. Dey, Nikos Zygouras
The directed polymer model at intermediate disorder regime was introduced by Alberts-Khanin-Quastel~\cite{AKQ12}. It was proved that at inverse temperature with t…