Related papers: Scaling limit for determinantal point processes on…
We consider the circular unitary ensemble with a Fisher-Hartwig singularity of both jump type and root type at $z=1$. A rescaling of the ensemble at the Fisher-Hartwig singularity leads to the confluent hypergeometric kernel. By studying…
Universal dimensionless quantities, such as Binder ratios and wrapping probabilities, play an important role in the study of critical phenomena. We study the finite-size scaling behavior of the wrapping probability for the Potts model in…
We consider two models of one-dimensional discrete random Schrodinger operators (H_n \psi)_l ={\psi}_{l-1}+{\psi}_{l +1}+v_l {\psi}_l, {\psi}_0={\psi}_{n+1}=0 in the cases v_k=\sigma {\omega}_k/\sqrt{n} and v_k=\sigma {\omega}_k/ \sqrt{k}.…
We investigate the limiting behavior of discrete determinantal point processes (DPPs) towards continuous DPPs when the size of the set to sample from goes to infinity. We propose a non-asymptotic characterization of this limit in terms of…
We present a solution to a problem suggested by Philippe Biane: We prove that a certain Plancherel-type probability distribution on partitions converges, as partitions get large, to a new determinantal random point process on the set…
The $\alpha$-determinant is a one-parameter generalisation of the standard determinant, with $\alpha=-1$ corresponding to the determinant, and $\alpha=1$ corresponding to the permanent. In this paper a simple limit procedure to construct…
In this paper, we study law of large numbers, central limit theorem, large and moderate deviations for INAR($\infty$) processes, which as a special case, includes both discrete-time linear Hawkes process and INAR(1) process in the…
The empirical spectral distribution of Hermitian $K \times K$-block random matrices converges to a deterministic density on the real line with a potential atom at the origin as the dimension of the blocks tends to infinity. In this model…
In this paper, we study the singularly perturbed Laguerre unitary ensemble $$ \frac{1}{Z_n} (\det M)^\alpha e^{- \textrm{tr}\, V_t(M)}dM, \qquad \alpha >0, $$ with $V_t(x) = x + t/x$, $x\in (0,+\infty)$ and $t>0$. Due to the effect of $t/x$…
We use SLE(6) paths to construct a process of continuum nonsimple loops in the plane and prove that this process coincides with the full continuum scaling limit of 2D critical site percolation on the triangular lattice -- that is, the…
We consider a shot-noise field defined on a stationary determinantal point process on $\mathbb{R}^d$ associated with i.i.d. amplitudes and a bounded response function, for which we investigate the scaling limits as the intensity of the…
We study scaling limits of a family of planar random growth processes in which clusters grow by the successive aggregation of small particles. In these models, clusters are encoded as a composition of conformal maps and the location of each…
We define a measure on tuples of partitions, called the symplectic Schur process, that should be regarded as the right analogue of the Schur process of Okounkov-Reshetikhin for the Cartan type C. The weights of our measure include factors…
Recent applications in queuing theory and statistical mechanics have isolated the process formed by the eigenvalues of successive minors of the GUE. Analogous eigenvalue processes, formed in general from the eigenvalues of nested sequences…
For a determinantal point process induced by the reproducing kernel of the weighted Bergman space $A^2(U, \omega)$ over a domain $U \subset \mathbb{C}^d$, we establish the mutual absolute continuity of reduced Palm measures of any order…
We consider the fluctuations of the number of eigenvalues of $n\times n$ random normal matrices depending on a potential $Q$ in a given set $A$. These eigenvalues are known to form a determinantal point process, and are known to accumulate…
The local eigenvalue statistics of large random matrices near a hard edge transitioning into a soft edge are described by the Bessel process associated with a large parameter $\alpha$. For this point process, we obtain 1) exponential moment…
Akemann, Ipsen, and Kieburg showed recently that the squared singular values of a product of M complex Ginibre matrices are distributed according to a determinantal point process. We introduce the notion of a polynomial ensemble and show…
We use SLE(6) paths to construct a process of continuum nonsimple loops in the plane and prove that this process coincides with the full continuum scaling limit of 2D critical site percolation on the triangular lattice -- that is, the…
The main result of this paper is that determinantal point processes on the real line corresponding to projection operators with integrable kernels are quasi-invariant, in the continuous case, under the group of diffeomorphisms with compact…