Related papers: A point process on the unit circle with antipodal …
We study the evolution leading to (or regressing from) a large fluctuation in a Statistical Mechanical system. We introduce and study analytically a simple model of many identically and independently distributed microscopic variables $n_m$…
A central limit theorem is shown for moderately interacting particles in the whole space. The interaction potential approximates singular attractive or repulsive potentials of sub-Coulomb type. It is proved that the fluctuations become…
Mean-field theories of the glass transition predict a phase transition to a dynamically arrested state, yet no such transition is observed in experiments or simulations of finite-dimensional systems. We resolve this long-standing…
Consider a supercritical Crump--Mode--Jagers process $(\mathcal Z_t^{\varphi})_{t \geq 0}$ counted with a random characteristic $\varphi$. Nerman's celebrated law of large numbers [Z. Wahrsch. Verw. Gebiete 57, 365--395, 1981] states that,…
We study analytically the correlations between the positions of tagged particles in the random average process, an interacting particle system in one dimension. We show that in the steady state the mean squared auto-fluctuation of a tracer…
It is well known that one can map certain properties of random matrices, fermionic gases, and zeros of the Riemann zeta function to a unique point process on the real line. Here we analytically provide exact generalizations of such a point…
We consider the one-dimensional stirring process on the segment $\{-N,\ldots,N\}$, coupled to boundary dynamics that inject particles from the right reservoir and remove particles from the left reservoir, each acting on a window of size…
We study two one-parameter families of point processes connected to random matrices: the Sine_beta and Sch_tau processes. The first one is the bulk point process limit for the Gaussian beta-ensemble. For beta=1, 2 and 4 it gives the limit…
For sub-additive ergodic processes $\{X_{m,n}\}$ with weak dependence, we analyze the rate of convergence of $\mathbb{E}X_{0,n}/n$ to its limit $g$. We define an exponent $\gamma$ given roughly by $\mathbb{E}X_{0,n} \sim ng + n^\gamma$,…
Experiments reveal that the superconductors $\text{UPt}_3$, $\text{U}_{1-x}\text{Th}_x\text{Be}_{13}$ and $\text{PrOs}_4\text{Sb}_{12}$ undergo two superconducting transitions in the absence of an applied magnetic field. The prevalence of…
The distribution of the properly renormalized gaps of $\sqrt{n} \,\mathrm{mod}\, 1$ with $n < N$ converges (when $N\rightarrow \infty$) to a non-standard limit distribution, as Elkies and McMullen proved in 2004 using techniques from…
The propagation of chaos and associated law of large numbers for mean-field interacting age-dependent Hawkes processes (when the number of processes n goes to +$\infty$) being granted by the study performed in (Chevallier, 2015), the aim of…
It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the existence of diffusion local time.…
In a view of recent proposals for the realization of anisotropic light-matter interaction in such platforms as (i) non-stationary or inductively and capacitively coupled superconducting qubits, (ii) atoms in crossed fields and (iii)…
We analyze nonequilibrium fluctuations of the averaging process on $\mathbb T_\varepsilon^d$, a continuous degenerate Gibbs sampler running over the edges of the discrete $d$-dimensional torus. We show that, if we start from a smooth…
In this paper it is demonstrated that a 1/f power spectrum appears in the process originated by the superposition of many similar single-sided RTN processes with the same relaxation time. The non-relaxed regime, the Gaussian nature and the…
The phase transition of the one-dimensional, diffusive pair contact process (PCPD) is investigated by N cluster mean-field approximations and high precision simulations. The N=3,4 cluster approximations exhibit smooth transition line to…
In this paper we study fluctuations of extreme particles of nonintersecting Brownian bridges starting from $a_1\leq a_2\leq \cdots \leq a_n$ at time $t=0$ and ending at $b_1\leq b_2\leq \cdots\leq b_n$ at time $t=1$, where…
Inspired by a recent paper of I. Grama, E. Le Page and M. Peign\'e, we consider a sequence $(g_n)_{n \geq 1}$ of i.i.d. random $d\times d$-matrices with non-negative entries and study the fluctuations of the process $(\log \vert g_n\cdots…
In this paper, we analyze the random fluctuations in a one dimensional stochastic homogenization problem and prove a central limit result, i.e., the first order fluctuations can be described by a Gaussian process that solves an SPDE with…