Within the framework of deist thought, how would you account for random events like particle decay?

Religion and science do not mix well and it is always religion which suffers. Religion (at least in the sense of Western religions) is about the interaction of man with God, not nucleus with God.

But beyond the question of the theological implications of random events (which I don't believe to even exist in properly formulated theology) the way you seem to understand randomness is probably more of a remnant of 19th century philosophy and science rather than the deeper insights of modern physics. The naive aspects of randomness that people like to refer to do not exist in nature, especially not in quantum mechanics where nothing is random but many things are uncertain. Before you can talk about this with any credibility you absolutely need to understand the difference.

In effect, I believe, you are fighting an uphill battle on two fronts with your question: you apply a non-existing definition or randomness in nature to a particularly fruitless discussion of religious beliefs. The result can only be a loss. Mostly of time and intellect on your part which you could use to learn what real science has to say about uncertainty in nuclear (and other) processes and what real theology has to say about God and our relationship with him, her or it.

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Within the framework of deist thought, how would you account for random events like particle decay?

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