We establish a novel type of connection between random walks and analytic number theory. Working with a random walk on the circle group $\mathbb{R}/\mathbb{Z}$ in which each step is a random...

We prove the limit theorem for paths of random walks with $n$ steps in $\mathbb{R}^d$ as $n$ and $d$ both go to infinity. For this, the paths are viewed as finite metric spaces equipped with the...

Smoluchowski-Kramers approximation in rough path topology with state-dependent damping is explored. The second-order Langevin equation has a form of fast-slow system after suitable...

We formulate a continuous-time competitive equilibrium model of irreversible capacity investment in which a continuum of heterogeneous producers supplies a single non-durable good subject to...

In this paper, we study the limiting distribution of the eigenvalues for random tridiagonal matrix models. The limiting distribution is well described by its moments. Here, an analytical approach...

We construct a family of infinite-dimensional reduced Heisenberg groups which can be viewed as infinite-dimensional homogeneous spaces. Such a space is an analogue of finite-dimensional reduced...

The ergodic theory of the open KPZ equation has seen significant progress in recent years, with explicit invariant measures described in a series of works by Corwin--Knizel, Barraquand--Le...

We introduce a multi-parameter family of random edge weights on the Aztec diamond graph, given by certain Gamma variables, and prove several results about the corresponding random dimer measures. ...

In this work, we establish the existence of solutions to stochastic differential equations on the Wasserstein space over a closed Riemannian manifold, under suitable regularity assumptions on the...