Related papers: A fixed-point approach to non-commutative central …
In this paper we study uniform versions of two limit theorems in random left truncation model (RLTM). The law of large numbers (LLN) and the central limit theorem (CLT) have been obtained under the bracketing entropy conditions in this…
This work improves the existing central limit theorems (CLTs) for geometric functionals of Gibbs processes in three aspects. First, we derive a CLT for weakly stabilizing functionals, thereby improving on the previously used assumption of…
We extend a free version of the Laha-Lukacs theorem to probability spaces with two-states. We then use this result to generalize a noncommutative CLT of Kargin to the two-state setting.
In this paper, we establish statistical results for a convex co-compact action of a free group on a CAT($-1$) space where we restrict to a non-trivial conjugacy class in the group. In particular, we obtain a central limit theorem where the…
We investigate possible renormalization-group fixed points at nonzero coupling in $\phi^3$ theories in six spacetime dimensions, using beta functions calculated to the four-loop level. We analyze three theories of this type, with (a) a…
Customers arrive at rate N times alpha on a network of N single server infinite buffer queues, choose L queues uniformly, join the shortest one, and are served there in turn at rate beta. We let N go to infinity.We prove a functional…
We prove, for any $\beta >0$, a central limit theorem for the fluctuations of linear statistics in the Sine-$\beta$ process, which is the infinite volume limit of the random microscopic behavior in the bulk of one-dimensional log-gases at…
The usual procedure of including a finite number of vertices in Non Perturbative Renormalization Group equations in order to obtain $n$-point correlation functions at finite momenta is analyzed. This is done by exploiting a general method…
The scaling behaviour of euclidean quantum gravity at an asymptotically safe critical point is studied by means of the exact renormalisation group. Gauge independence is ensured via a specific parameterisation of metric fluctuations…
The distribution of descents in fixed conjugacy classes of $S_n$ has been studied, and it is shown that its moments have interesting properties. Fulman proved that the descent numbers of permutations in conjugacy classes with large cycles…
When the underlying random variables are Gaussian, the classical Central Limit Theorem (CLT) is trivial, but the functional CLT is not. The objective of the paper is to investigate the functional CLT for stationary Gaussian processes in the…
We discuss CLT for the global and local linear statistics of random matrices from classical compact groups. The main part of our proofs are certain combinatorial identities much in the spirit of works by Kac and Spohn.
We introduce the notion of a random relaxed asymptotic contraction in the setting of random normed modules. The contraction condition employs two quasi-metrics that are built directly from the random operator: a lower quasi-metric which…
By the Lindeberg-L\'evy central limit theorem, standardized partial sums of a sequence of mutually independent and identically distributed random variables converge in law to the standard normal distribution. It is known that mutual…
The main aim of this paper is to solve an inverse source problem for a general nonlinear hyperbolic equation. Combining the quasi-reversibility method and a suitable Carleman weight function, we define a map of which fixed point is the…
The infinite disorder fixed point of the random transverse-field Ising model is expected to control the critical behavior of a large class of random quantum and stochastic systems having an order parameter with discrete symmetry. Here we…
We study renormalization group multicritical fixed points in the $\epsilon$-expansion of scalar field theories characterized by the symmetry of the (hyper)cubic point group $H_N$. After reviewing the algebra of $H_N$-invariant polynomials…
Cosmological perturbation theory is known to converge poorly for predicting the spherical collapse and void evolution of collisionless matter. Using the exact parametric solution as a testing ground, we develop two asymptotic methods in…
We prove annealed central limit theorems for finite pattern counts in the measurement record of discrete-time quantum trajectories generated by repeated measurements in a disordered environment. Under summable mixing assumptions on the…
It is well-known that, on a purely algebraic level, a simplified algebraic version of the Central Limit Theorem (CLT) can be proved in the framework of a noncommutative probability space, under the hypotheses that the sequence of…