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Space-time fractional stochastic partial differential equations driven by L\'evy white noise
Yuhui Guo, Jiang-Lun Wu
https://arxiv.org/abs/2506.12834 h…

Space-time fractional stochastic partial differential equations driven by Lévy white noise
This paper is concerned with the following space-time fractional stochastic nonlinear partial differential equation \begin{equation*} \left(\partial_t^β+\fracν{2}\left(-Δ\right)^{α/ 2}\right) u=I_{t}^γ\Big[ f(t,x,u)-\sum_{i=1}^{d} \frac{\partial}{\partial x_i} q_i(t,x,u)+ σ(t,x,u) F_{t,x}\Big] \end{equation*} for a random field $u(t,x):[0,\infty)\times\mathbb{R}^d \mapsto\mathbb{R}$, where $α>0, β\in(0,2), γ\ge0, ν>0, F_{t,x}$ is a Lévy space-time white noise, $I_{t}^γ$ stands for…

An elementary proof of existence and uniqueness of stationary distributions for irreducible Markov chains
Rinaldo B. Schinazi
https://arxiv.org/abs/2506.13662

An elementary proof of existence and uniqueness of stationary distributions for irreducible Markov chains
Consider an $n\times n$ matrix $P$ with the following properties. All entries in $P$ are positive or $0$, the sum of each row is 1 and for all $i$ and $j$ in $\{1,\dots,n\}$ there exists a natural number $k$ such that the $(i,j)$ entry of the matrix $P^k$ is strictly positive. Then, there exists a unique row vector $v$ with only strictly positive entries, whose sum of entries is 1 and such that $vP=P$. We present a proof of this well-known result that uses only basic algebra and the Bolzano-Wei…

Character degrees in principal blocks for distinct primes
Annika Bartelt
https://arxiv.org/abs/2506.06860 https://arxiv.org/pdf/2506.…

Character degrees in principal blocks for distinct primes
Let $G$ be a finite group of order divisible by two distinct primes $p$ and $q$. We show that $G$ possesses a non-trivial irreducible character of degree not divisible by $p$ nor $q$ lying in both the principal $p$- and $q$-block whenever $G$ is one of the following: an alternating group $\mathfrak{A}_n$, $n\geq 4$, a symmetric group $\mathfrak{S}_n$, $n\geq 3$, or a finite simple classical group of type A, B, or C, defined in characteristic distinct from $p$ and $q$. This extends earlier resul…

Admitted symmetries of Backward Stochastic Differential Equations
Anas Ouknine, Paul Lescot
https://arxiv.org/abs/2506.10650 https://…

Admitted symmetries of Backward Stochastic Differential Equations
In this article, we introduce the concept of admitted Lie group of transformations for both backward stochastic differential equations (BSDEs) and forward backward stochastic differential equations (FBSDEs), following the approach of Meleshko et al. An application to BSDE is presented.

Schramm-Loewner evolution contains a topological Sierpi\'nski carpet when $\kappa$ is close to 8
Haoyu Liu, Zijie Zhuang
https://arxiv.org/abs/2506.09609

Schramm-Loewner evolution contains a topological Sierpiński carpet when $κ$ is close to 8
We consider the Schramm-Loewner evolution (SLE$_κ$) for $κ\in (4,8)$, which is the regime where the curve is self-intersecting but not space-filling. We show that there exists $δ_0>0$ such that for $κ\in (8 - δ_0,8)$, the range of an SLE$_κ$ curve almost surely contains a topological Sierpiński carpet. Combined with a result of Ntalampekos (2021), this implies that in this parameter range, SLE$_κ$ is almost surely conformally non-removable, and the conformal welding problem for SLE$_κ$…

The stochastic heat inclusion with fractional time driven by time-space Brownian and L\'evy white noise
Olfa Draouil, Rahma Yasmina Moulay Hachemi, Bernt {\O}ksendal
https://arxiv.org/abs/2506.08275

The stochastic heat inclusion with fractional time driven by time-space Brownian and Lévy white noise
We study a time-fractional stochastic heat inclusion driven by additive time-space Brownian and Lévy white noise. The fractional time derivative is interpreted as the Caputo derivative of order $α\in (0,2).$ We show the following: \\ a) If a solution exists, then it is a fixed point of a specific set-valued map.\\ b) Conversely, any fixed point of this map is a solution of the heat inclusion.\\ c) Finally, we show that there is at least one fixed point of this map, thereby proving that there …

Dynamic Space Filling
P. L. Krapivsky
https://arxiv.org/abs/2506.01128 https://arxiv.org/pdf/2506.01128

Dynamic Space Filling
Dynamic space filling (DSF) is a stochastic process defined on any connected graph. Each vertex can host an arbitrary number of particles forming a pile, with every arriving particle landing on the top of the pile. Particles in a pile, except for the particle at the bottom, can hop to neighboring vertices. Eligible particles hop independently and stochastically, with the overall hopping rate set to unity for every eligible particle at every vertex. When the number of vertices in a graph is equa…

The half-space KPZ line ensemble and its scaling limit
Sayan Das, Christian Serio
https://arxiv.org/abs/2506.07939 https://arxiv.org/…

The half-space KPZ line ensemble and its scaling limit
For each $α\in \mathbb{R}$, $t \geq 1$, we show that there exists a unique $\mathbb{N}$-indexed line ensemble of random continuous curves $\mathbb{R}_{\le 0} \to \mathbb{R}$ with the following properties: (1) The top curve is distributed as the time-$t$ Cole--Hopf solution to the half-space KPZ equation with narrow wedge initial condition and Neumann boundary condition with parameter $α$. (2) The line ensemble satisfies a one-sided resampling invariance property, involving softly non-inte…

On the rank of a random symmetric matrix in the large deviation regime
Yi Han
https://arxiv.org/abs/2506.01155 https://arxiv.org/pdf/…

On the rank of a random symmetric matrix in the large deviation regime
Let $A$ be an $n\times n$ random symmetric matrix with independent identically distributed subgaussian entries of unit variance. We prove the following large deviation inequality for the rank of $A$: for all $1\leq k\leq c\sqrt{n}$, $$\mathbb{P}(\operatorname{Rank}(A)\geq n-k)\geq 1-\exp(-c'kn),$$ for some fixed constants $c,c'>0$. A similar large deviation inequality is proven for the rank of the adjacency matrix of dense Erdos-Renyi graphs. This corank estimate enhances the recent breakthroug…