Related papers: Continuous Differentiability of Renormalized Inter…

Let $B^{H_1}$ and $\tilde{B}^{H_2}$ be two independent fractional Brownian motions on ${\mathbb R}$ with respective indices $H_i\in (0,1)$ and $H_1\leq H_2$. In this paper, we consider their intersection local time $\ell_t(a)$. We show that…

Bassino et al. (arXiv:1907.08517) have shown that uniform random co-graphs (graphs without induced $P_4$) of size $n$ converge to a certain non-deterministic graphon. The edge-density of this graphon is a random variable $\Lambda \in [0,1]$…

We define renormalized intersection local times for random interlacements of L\'evy processes in R^{d} and prove an isomorphism theorem relating renormalized intersection local times with associated Wick polynomials.

Let $(X_t,t\geq0)$ be a continuous time simple random walk on $\mathbb{Z}^d$ ($d\geq3$), and let $l_T(x)$ be the time spent by $(X_t,t\geq0)$ on the site $x$ up to time $T$. We prove a large deviations principle for the $q$-fold…

We study the object formally defined as \gamma\big([0,t]^{2}\big)=\int\int_{[0,t]^{2}} | X_{s}- X_{r}|^{-\sigma} dr ds-E\int\int_{[0,t]^{2}} | X_{s}- X_{r}|^{-\sigma} dr ds, where $X_{t}$ is the symmetric stable processes of index…

The generalized grey Brownian motion is a time continuous self-similar with stationary increments stochastic process whose one dimensional distributions are the fundamental solutions of a stretched time fractional differential equation.…

We study the persistence probability for some two-sided discrete-time Gaussian sequences that are discrete-time analogs of fractional Brownian motion and integrated fractional Brownian motion, respectively. Our results extend the…

In this article we calculate the third and fourth moment of the renormalized intersection local time of a planar Brownian motion. The third moment is calculated anlaytically, the fourth moment numerically. For the closed planar random walk…

Let $\{L^{x}_{t} ; (x,t)\in R^{1}\times R^{1}_{+}\}$ denote the local time of Brownian motion and \[ \alpha_{t}:=\int_{-\infty}^{\infty} (L^{x}_{t})^{2} dx . \] Let $\eta=N(0,1)$ be independent of $\alpha_{t}$. For each fixed $t$ \[…

We study the spectrum of the kinetic Brownian motion in the space of $d\times d$ Hermitian matrices, $d\geq2$. We show that the eigenvalues stay distinct for all times, and that the process $\Lambda$ of eigenvalues is a kinetic diffusion…

Let B_t^H be a d-dimensional fractional Brownian motion with Hurst parameter H\in(0,1). Assume d\geq2. We prove that the renormalized self-intersection local time\ell=\int_0^T\int_0^t\delta(B_t^H-B_s^H) ds dt -E\biggl(\int_0^T\int_0^t\delta…

Consider a one-dimensional stepping stone model with colonies of size $M$ and per-generation migration probability $\nu$, or a voter model on $\mathbb{Z}$ in which interactions occur over a distance of order $K$. Sample one individual at…

We introduce a class of kinetic and anisotropic random motions $(x_t^{\sigma},v_t^{\sigma})_{t \geq 0}$ on the unit tangent bundle $T^1 \mathcal M$ of a general Riemannian manifold $(\mathcal M,g)$, where $\sigma$ is a positive parameter…

We characterize complete nonnegatively curved steady gradient soliton with curvature in L^1. We show that there are isometric to a product (R^2,g_{cigar}) times(R^{n-2}, eucl))/Gamma where Gamma is a Bieberbach group of rank n-2. We prove…

We study a continuous pathwise local time of order p for continuous functions with finite p-th variation along a sequence of time partitions, for even integers p >= 2. With this notion, we establish a Tanaka-type change of variable formula,…

We establish an integral test describing the exact cut-off between recurrence and transience for normally reflected Brownian motion in certain unbounded domains in a class of warped product manifolds. Besides extending a previous result by…

In this note we consider the time of the collision $\tau$ for $n$ independent Brownian motions $X^1_t,...,X_t^n$ with drifts $a_1,...,a_n$, each starting from $x=(x_1,...,x_n)$, where $x_1<...<x_n$. We show the exact asymptotics of…

The problem of diagonalization of Hamiltonians of N-dimensional boson systems by means of time-dependent canonical transformations (CT) is considered, the case of quadratic Hamiltonians being treated in greater detail. The unitary generator…

We consider Random Walk in Random Scenery, denoted $X_n$, where the random walk is symmetric on $Z^d$, with $d>4$, and the random field is made up of i.i.d random variables with a stretched exponential tail decay, with exponent $\alpha$…

We consider the paths of a Gaussian random process $x(t)$, $x(0)=0$ not exceeding a fixed positive level over a large time interval $(0,T)$, $T\gg 1$. The probability $p(T)$ of such event is frequently a regularly varying function at…