Related papers: Two Bessel Bridges Conditioned Never to Collide, D…

We consider a class of stochastic processes containing the classical and well-studied class of Squared Bessel processes. Our model, however, allows the dimension be a function of the time. We first give some classical results in a larger…

The interplay between two-dimensional percolation growth models and one-dimensional particle processes has been a fruitful source of interesting mathematical phenomena. In this paper we develop a connection between the construction of…

We generalise the integration by parts formulae obtained in arXiv:1811.00518v5 [math.PR] to Bessel bridges on $[0,1]$ with arbitrary boundary values, as well as Bessel processes with arbitrary initial conditions. This allows us to write,…

We develop an effective field theory to understand collective modes of a three-dimensional two-component Fermi superfluid with dipolar inter-particle interactions, which are modeled by an idealized separable potential. We first examine the…

Conrey, Farmer, Keating, Rubinstein, and Snaith, recently conjectured formulas for the full asymptotics of the moments of $L$-functions. In the case of the Riemann zeta function, their conjecture states that the $2k$-th absolute moment of…

We study a one-phase Bernoulli free boundary problem with weight function admitting a discontinuity along a smooth jump interface. In any dimension $N\ge 2$, we show the $C^{1, \alpha}$ regularity of the free boundary outside of a singular…

We give a general expression for the Weyl tensor two-point function in a general Friedmann-Lema\^itre-Robertson-Walker spacetime. We work in reduced phase space for the perturbations, i.e., quantize only the dynamical degrees of freedom…

A discrete model of Brownian sticky flows on the unit circle is described: it is constructed with products of Beta matrices on the discrete torus. Sticky flows are defined by their ``moments'' which are consistent systems of transition…

We study the moments of the partial transpose of the reduced density matrix of two intervals for the free massless Dirac fermion. By means of a direct calculation based on coherent state path integral, we find an analytic form for these…

For a model 1d asymmetric double-well potential we calculated so-called survival probability (i.e. the probability for a particle initially localised in one well to remain there). We use a semiclassical (WKB) solution of Schroedinger…

Bessel process is defined as the radial part of the Brownian motion (BM) in the $D$-dimensional space, and is considered as a one-parameter family of one-dimensional diffusion processes indexed by $D$, BES$^{(D)}$. It is well-known that…

We review the role of dual pairs in mechanics and use them to derive particle-like solutions to regularized incompressible fluid systems. In our case we have a dual pair resulting from the action of diffeomorphisms on point particles…

In this paper, we study the lifespan and continuation criteria of several two-dimensional incompressible fluid models. Motivated by a novel energy-vorticity formulation, combining linear transport estimate and a bootstrap argument, we are…

Let $ \mathfrak{f} $ run over the space $ H_{4k} $ of primitive cusp forms of level one and weight $ 4k $, $ k \in N $. We prove an explicit formula for the mixed moment of the Hecke $ L $-function $ L(\mathfrak{f}, 1/2) $ and the symmetric…

The $2 q$-th pseudomoment $\Psi_{2q,\alpha}(x)$ of the $\alpha$-th power of the Riemann zeta function is defined to be the $2 q$-th moment of the partial sum up to $x$ of $\zeta^\alpha$ on the critical line. Using probabilistic methods of…

Motivated by the polynuclear growth model, we consider a Brownian bridge b(t) with b(\pm T)=0 conditioned to stay above the semicircle c_T(t)=\sqrtT^2-t^2. In the limit of large T, the fluctuation scale of b(t)-c_T(t) is T^{1/3} and its…

In a recent paper with Sprang and Zudilin, the following result was proved: if $a$ is large enough in terms of $\varepsilon>0$, then at least $2^{(1-\varepsilon)\frac{\log a}{\log \log a}}$ values of the Riemann zeta function at odd…

In this paper, we consider the initial and boundary value problem of Ericksen-Leslie system modeling nematic liquid crystal flows in dimension three. Two examples of singularity at finite time are constructed. The first example is…

Using the method of continuous constructive renormalization group around the Fermi surface, it is proved that a jellium two-dimensional interacting system of Fermions at low temperature $T$ remains analytic in the coupling constant…

We discuss moments of the Riemann zeta-function in this paper. The purpose of this paper is to give an upper bound of exponential moments of the logarithm of the Riemann zeta-function twisted by arguments. Our results contain an improvement…