论文标题
扩散限制的歼灭系统中的粒子密度
Particle density in diffusion-limited annihilating systems
论文作者
论文摘要
将$ a $零件放置在图表的每个站点，概率$ p $，否则将$ b $ - 零件放置。 $ a $ - 和$ b $ - 粒子分别以$λ_a$和$λ_b$进行独立的连续时间随机步行，并在与相反类型的粒子碰撞时消灭。 Bramson和Lebowitz在1990年代初研究了设置$λ_A=λ_b$。尽管最近取得了进展，但当$λ_A\neqλ_b$时，许多基本问题仍未得到解决。对于关键情况，低维整数晶格上的$ p = 1/2 $，我们对与物理学家预测相匹配的原点的预期粒子数量下降。对于整数和额外的常规树的$λ_b= 0 $的过程，我们在较重要的临界点和接近临界点的预期总职业时间内给出了清晰的上限和下限。
Place an $A$-particle at each site of a graph independently with probability $p$ and otherwise place a $B$-particle. $A$- and $B$-particles perform independent continuous time random walks at rates $λ_A$ and $λ_B$, respectively, and annihilate upon colliding with a particle of opposite type. Bramson and Lebowitz studied the setting $λ_A = λ_B$ in the early 1990s. Despite recent progress, many basic questions remain unanswered for when $λ_A \neq λ_B$. For the critical case $p=1/2$ on low-dimensional integer lattices, we give a lower bound on the expected number of particles at the origin that matches physicists' predictions. For the process with $λ_B=0$ on the integers and the bidirected regular tree, we give sharp upper and lower bounds for the expected total occupation time of the root at and approaching criticality.
